Hampshire, who had won the toss and elected to bat, survived a testing first hour, albeit Ian Holland was dropped without scoring at third slip and Morne Morkel rattled through five successive maidens.
But the introduction of first-change pair Clarke and Jordan Clark decimated the hosts’ top order – with the pair’s morning spell seeing five wickets fall for 31 runs.
Clark needed only six balls to tumble Holland’s off stump before Clarke had Felix Organ caught flashing to third slip and Tom Alsop castled in successive overs – as the Hotel End went 9.3 overs before seeing a run.
Veteran Clarke then claimed his 500th first-class wicket, which coincided with his 450th Championship scalp, when pushed to second slip, leaving Hampshire 26 for four.
James Vince attempted to fight the swing by smashing a six over square leg before producing back-to-back boundaries – but Clark had the last laugh as Jamie Smith hung on at point.
Conor McKerr had Liam Dawson caught behind soon after lunch, before Clarke completed his five-for when the enterprising Aneurin Donald’s leading-edge landed at mid-off and Keith Barker was caught at gully.
Kyle Abbott and Lewis McManus provided some rearguard action for the hosts as they put on 45 for the ninth wicket – before the former was bowled by Jordan Clark, who bagged three for 50, and the latter was lbw to Morne Morkel to conclude the innings.
Surrey’s batsmen didn’t find the conditions any easier to battle through as they collapsed to 37 for three and 61 for five.
Fidel Edwards made the breakthrough in the sixth over when, unlike the pattern of wickets of the day, he bounced Mark Stoneman out, with Vince pouching a simple catch.
An over later Dean Elgar edged Kyle Abbott behind, before Scott Borthwick and Jamie Smith both poked Barker to Dawson at second slip.
England hopeful Ben Foakes was the next to depart to give Barker his third.
But Pope, along with Clarke, hurried the scoring along with a 72 stand for the sixth wicket, with several eye-catching shots nestled among some clever running.
Pope departed in the twilight when Holland had him lbw, before McKerr was leg-before to Abbott to the last ball of the day - Surrey still behind but by just six runs.
James Vince completely changed the complexion of Hampshire’s Specsavers County Championship clash with Surrey with an outrageous 59-ball 91.
A green-tinged Ageas Bowl wicket had seen 23 wickets fall in a day and a half before Vince arrived at the crease to flail the ball to all points of the Ageas Bowl.
Vince, whose efforts may have caught the England selectors’ eyes ahead of tours to New Zealand and South Africa this winter, smacked 18 boundaries in his exceptional knock.
The Hampshire captain had moved down to No.5 in the batting order for this match, with a decision to protect him from the new ball.
He was guided through his swashbuckling innings by Sam Northeast, who scored 73, while Felix Organ had earlier recorded his third half-century of the season.
Surrey started the second day trailing by six runs but quickly found themselves in the black, only to lose their remaining three wickets in six overs.
Rikki Clarke was lbw to Kyle Abbott following a high-quality 40 and Morne Morkel was run out before Keith Barker returned his best figures for Hampshire when he castled Amar Virdi. The left-arm fast bowler posting four for 38.
Hampshire, who gave up a 13 run first-innings deficit, appeared as if they were on course to replicate their first-innings collapse when they were bowled out for 149, when they slumped to 39 for two.
Ian Holland left a Morkel delivery which jagged back and clipped the top of the off-stump before Tom Alsop was caught behind.
But Organ steadied the ship, alongside Northeast, with a patient innings which belied his 20-years, while still taking the opportunity to ticked the runs along.
The academy graduate has scored a century and two fifties in three Championship appearances this season, with his most recent visit to the milestone coming from 73 balls and brought up with a controlled edge to the third man boundary.
His innings ended on 54 when he swiped and edged to Clarke at first slip, to bring Vince to the crease.
From the moment he carved an edge over the slips, Vince looked at home at the wicket – with back-foot pushes, typically cover drives and clips off the pads among the plentiful fours from his bat.
He reached fifty in 37 balls and bludgeoned his way to 91 before he edged Amar Virdi to first slip – the second time he had departed in the nervy 90s in his Championship career.
Among Vince’s carnage, Northeast, who has 930 Championship runs this season, had played a gem of an innings at the other end.
The former Kent batsman had played a part in the 129 runs in 16.3overs with Vince before he reached a slightly more sedate 71-ball 50.
Northeast departed when he edged to Clarke before Aneurin Donald was bowled by Virdi. But Liam Dawson’s caressing and Lewis McManus’ hitting, Hampshire’s lead reached 283.
Due to a rain delay either side of tea and bad light stopping play early, 32 overs were lost from the day.
Felix Organ claimed his maiden five-wicket haul as Hampshire secured a comprehensive 272-run Specsavers County Championship victory against Surrey at the Ageas Bowl.
Usually an opening batsman, Organ celebrated figures of five for 25 on his fifth first-class appearance– having come on to bowl earlier than planned due to the umpires declaring it too dark for fast bowling.
Organ, who had scored a half-century with the bat earlier in the match, found good turn as he dismissed Ben Foakes, Jamie Smith, Rikki Clarke, Conor McKerr and Jordan Clark as Surrey were skittled for 151.
Hampshire, who hadn’t tasted Championship victory since winning on the Isle of Wight in May, took 21 points to reigning champion Surrey’s three – although both sides were safe ahead of the match, with no hope of challenging for the title.
It was also Hampshire's first victory over Surrey at the Ageas Bowl.
Surrey were given an imposing target of 424 in a smidgen under five sessions, knowing that a solid start was needed to platform any hopes of victory.
But that didn’t come as Keith Barker struck with his first delivery, the seventh of the innings, as Dean Elgar was caught behind off the face of the bat while attempting to leave.
In the fifth over, Kyle Abbott found Scott Borthwick attempting a straight drive but a slight nip away off the seam saw another nick through to Lewis McManus’ gloves.
That left the visitors 12 for two, and it became 37 for three six overs later as Mark Stoneman walked across his stumps and Ian Holland dislodged his leg stump.
Ollie Pope caressed a fine 40 but he too edged Abbott behind – the England hopeful furious with his nothing shot as he trudged back to the dressing room.
As bad light descended on the Ageas Bowl, the umpires advised that only slow bowling could be utilised, which Organ used to his advantage.
The 20-year-old off-spinner wouldn’t have been too proud of the long hop that Foakes lunged to Sam Northeast at mid-wicket but beautifully deceived Smith before McManus stumped him.
Organ then lured Clarke into an attacking hoick, which picked out Holland at deep midwicket, and McKerr was lbw.
Clark top-edged to Fidel Edwards to give Organ his fifth and Liam Dawson castled Morne Morkel for his 200th first-class wicket to wrap up the three-day triumph.
Earlier, McManus and Dawson both completed half-centuries as Hampshire extended their lead with 100 day three runs.
Dawson, who was 39 overnight, reached the milestone first from 82 balls, before McManus followed in two deliveries more slightly later – the pair putting on 117 for the seventh wicket.
The duo were both dropped, McManus on 21 at gully and Dawson on 78 at cover, before the second new ball dismissed them.
The former brilliantly caught by Ollie Pope at gully 61 while the latter moved to 88 before he was snaffled by Rikki Clarke at first slip.
Barker and Abbott scored 16 and 18 runs respectively to see the tail wag – but both departed, caught behind and stumped, to round off the innings.