Durham defeated Surrey by 152 runs in the Durham 262 and 1 for 1 trail Surrey 415 match. Patel scored 134 runs, Lawes scored 58 runs, Burns scored 55 runs, and de Leede took 4 wickets for 106 runs.
Ryan Patel's career-best 134 guided Surrey to 415 and the vital advantage of a 153-run first innings lead against Durham at the Kia Oval.
And Dan Worrall then had nightwatchman Callum Parkinson superbly held by Conor McKerr at third slip from the first ball of Durham's second innings as, in two overs' batting, they finished on 1 for 1.
Patel, who batted for just short of five hours in a crucial anchor role before being caught on the deep midwicket boundary, took the game away from Durham in an eighth wicket stand of 92 in 19 overs with Tom Lawes.
The pair began by attacking the second new ball, quickly tilting the balance of a previously hard-fought day sharply towards Surrey, the County Championship leaders and favourites for a third successive title.
Lawes, the richly-talented 21-year-old allrounder, struck a six and six fours in a confident 58, only his second first-class score above fifty and also a career-best.
If they had taken their catches, however, Durham might have put themselves into a strong position - especially as Patel was the main beneficiary of their largesse when he was dropped on 19 and 70.
For 26-year-old Patel, who faced 183 balls and hit three sixes and 14 fours, it was a fifth first-class hundred and his second of the season, while Tom Curran also survived two edges into the slip cordon early on in an 81-ball stay for 22 and Rory Burns was dropped on 43 soon after the start of the second day's play.
Durham, despite their fielding lapses, performed creditably with the ball to make run-scoring hard work for Surrey until Patel and Lawes pulled away.
Surrey resumed on 52 without loss, in reply to Durham's first innings 262, and Burns - after adding just three to his overnight 40 - was spilled in the slips off Daniel Hogg.
Dom Sibley helped Burns take their opening stand to an excellent 87 before, on 26, edging slippery seamer Bas de Leede low to first slip while Burns had reached 55 when he was bowled by a magnificent delivery from Barbadian paceman Chemar Holder.
A mini-collapse continued, with Surrey losing three wickets in five overs as Dan Lawrence (6) followed up one glorious cover boundary by pushing at a ball from de Leede and, like Sibley, snicking low to David Bedingham at first slip.
But, from 110 for 3, Patel and Ben Foakes steadied the innings with a partnership of 47 - with Foakes needing on-field treatment after being hit on the hand by Hogg.
On 17, however, Foakes was adjudged to have feathered a catch to keeper Ollie Robinson and the impressive de Leede, who finished with 4 for 106, struck again when he fired in a yorker to hit Sam Curran (8) on the boot and win an lbw appeal that left Surrey 169 for 5.
Dan Worrall struck with the first ball of Durham's second innings
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Getty Images for Surrey CCC
Tom Curran began aggressively but saw one edge off Holder burst through Bedingham's hands at first slip and run away for four and then another fail to be taken due to Robinson initially going for the ball but then leaving it to a surprised Bedingham.
After that, Curran concentrated on supporting Patel in a partnership that eventually realised 63 before being squared up by a fine ball from left-arm spinner Parkinson that clipped his off stump.
Then came perhaps the key moment of the day when Patel, on 70, hooked a short one from de Leede straight to deep square leg where Stanley McAlindon, a substitute fielder, got in a tangle and allowed the ball to fly through his hands and over the rope for six.
Patel, who had earlier survived on 19 when James Minto failed to hold on to a skimming drive at Parkinson at short midwicket, then extra cover drove de Leede's next ball for four to go to 80 and, in the next over, back-to-back boundaries by Jordan Clark off Parkinson took Surrey into the lead.
Clark made 22 before pulling Holder to deep square leg but Patel, with further legside sixes off Hogg and Minto, was then joined by Lawes in what could well be a match-defining partnership.
McKerr skied Minto to Robinson on 10 to give the 16-year-old left-arm quick a maiden first-class wicket and last man Worrall (6 not out) stayed to ensure Surrey a fourth batting bonus point and until Lawes, ironically given Durham's previous missed catches, was quite brilliantly held by a diving Alex Lees at long off as Minto finished with 2 for 78.