The Division One leaders completed a fifth win from seven matches this summer shortly after lunch as they chased a target of 228 with a significant amount of comfort having started the day on 89 without loss.
Burns, who hit 15 fours in 146 balls, shared 99 for the first wicket with Mark Stoneman (32) and 47 for the second with Scott Borthwick before falling three short of a third Championship century this season.
At that stage, 40 minutes before lunch, Surrey needed 82 more, and they advanced calmly.
Borthwick, who shared 74 with third-wicket partner Ryan Patel, contributed 62 off 112 balls. Patel finished 24 not out.
This was a match which swung back and forth, but decisively on day three when Yorkshire, who led by 75, were bowled out for 152 in their second innings. Morne Morkel impressed with 5-39.
Surrey gained 21 points to Yorkshire’s six and will have to wait on second-placed Nottinghamshire’s result against Worcestershire before knowing the extent of their lead at the halfway stage of the campaign.
The White Rose have now lost three of their seven matches and are, realistically, looking down rather than up.
They are likely to end the round second-bottom in the table, albeit with a game in hand on Hampshire and Lancashire directly above them.
Surrey’s four most recent successful away chases have all been on out-grounds at Colwyn Bay, Beckenham, Colchester and here. And they will hope another statistic proves to be a good omen.
The last five teams who have gone on to win the Championship have all won matches here – Durham in 2013, Yorkshire in ’14 and ’15, Middlesex in ’16 and Essex last summer.
Yorkshire started pretty well with the ball in the opening hour of the day, but they needed more than the wicket of Stoneman lbw to Ben Coad without adding to his overnight total.
For Stoneman, his 32 was a season’s best Championship score.
Burns started day four unbeaten on 55 and continued to drive well and play confidently through mid-wicket before uppercutting a short and wide Tim Bresnan delivery to deep backward point as the score slipped to 146-2 after 43 overs.
The left-hander is now the leading run-scorer in Division One with 722 at 65.63, including two hundreds and three fifties, and has overtaken team-mate Ollie Pope.
At lunch, Surrey needed 39 more with Borthwick unbeaten on 46. He reached 50 in the second over after lunch off 87 balls, but he was later bowled by Jack Leaning’s part-time spin with only eight needed. Theunis de Bruyn hit the winning runs.
Surrey face Nottinghamshire at Trent Bridge in their next match late next month (July 22), while Yorkshire travel to Emirates Old Trafford for the first Roses clash of 2018.