The White Rose, starting the day 65 runs behind at 89 for two in their second innings - following-on after being dismissed for 179 in reply to Surrey's first-innings 333 - were bowled out again for 208 with Dan Worrall taking four for 61.
That left Surrey needing just 55 for victory, knowing that second-placed Hampshire had already lost to Kent at Southampton, and their 22-point win took them 27 clear at the top of Division One - an unassailable lead with just one game left.
It took captain Rory Burns and his fellow opener Ryan Patel only 37 balls to knock off the runs required, with the former England batter pulling his opposite number Jonny Tattersall, who took off his wicketkeeping pads to purvey some leg-breaks, for four to take Surrey home.
It was Surrey's eighth win from 13 matches and they remain the only county from both divisions to remain unbeaten in what has been a triumphant campaign.
Yorkshire's chances of turning the match around suffered an almost immediate blow when Cameron Steel, surprisingly given the first over of the day from the Vauxhall End, turned his googly appreciably to bowl Tom Kohler-Cadmore for 11 through a back foot defensive gate with his sixth ball.
Adam Lyth, who had battled to 36 on the second evening, resisted for almost an hour in the company of Will Fraine before the two fell in quick succession.
Fraine went for 13, bowled by a ball from Jordan Clark which jagged back off the seam and may have brushed his right elbow before cannoning into the middle and off stumps, and then Lyth departed for 46 as Kemar Roach was at last rewarded for a testing spell from the Pavilion End.
West Indies Test paceman Roach, in his seventh over of the morning, swung one away from left-hander Lyth, from around the wicket, to have the former England opener caught by Patel at third slip.
That left Yorkshire 116 for five and, 11 overs and 34 runs later, Tattersall's 21 ended when he touched a lifting leg-side ball from Jamie Overton to wicketkeeper Ben Foakes.
Soon after lunch Worrall angled one that kept a little low into Jordan Thompson's pads, from around the wicket, to have the left-hander leg-before for eight.
And when Dom Bess, who had fought hard for his 43 from 71 balls, could only fend off a steeply rising ball from Roach to Foakes, making good ground to his left to take the catch, the end was nigh for Yorkshire's second innings.
In the next over, indeed, Worrall pegged back Ben Mike's off stump with a perfect outswinger, the all-rounder departing for a 14 which had included a second-ball pull for six off the same bowler.
Worrall hit last man Steven Patterson's off stump to finish off the innings, leaving Burns to take three fours off Ben Coad's opening over as he and Patel knocked off the runs with a flourish, scoring 30 and 19 not out respectively.