This followed their dismissal for 147 in the first innings as they struggled to cope with a testing wicket and conditions that aided swing. The key difference between the sides was that Yorkshire bowled better for longer.
The combination of results could not have been worse for Adam Hollioake's team, who find themselves dislodged from their long-established perch at the top of the table by Leicestershire, successful against Warwickshire at Edgbaston yesterday.
Leicestershire, who meet Surrey at The Oval in 12 days' time, have 244 points, a lead of five, with Lancashire three points behind Surrey in third following their victory over Derbyshire. Gloucestershire and Yorkshire, who retain an outsider's chance by virtue of yesterday's win, are equal fourth with 223 points.
Even with Darren Gough absent, nursing a hamstring injury, Surrey never looked like surviving the 88 overs left in the contest after Yorkshire asked them to chase 300 to win on the final day.
The only real resistance was offered by Ben Hollioake, who hit a challenging 60 off 67 balls, including 13 boundaries, as Silverwood (5 for 30), Hamilton (4 for 22) and Matthew Hoggard steadily cut Surrey down.
Silverwood began the destruction by removing both openers in his first four overs, trapping Mark Butcher leg before wicket with an inswinger before Ian Ward sliced a drive straight to Michael Vaughan at backward point.
Hamilton then struck a vital blow by having Alec Stewart caught by Craig White at first slip and in the last over before lunch Ally Brown edged a Hoggard outswinger into the gloves of Richard Blakey.
The afternoon quickly brought two more successes for Hamilton, who had Nadeem Shahid lbw and deceived Adam Hollioake into giving a catch off a slower ball, leaving Surrey in dire straits at 63 for 6 with still 59 overs to survive.
Then came a partnership of 54 between Ben Hollioake and Jonathan Batty, who battled for 55 minutes for his nine, but the return of Silverwood at the Kirkstall Lane End brought about his downfall and that of Martin Bicknell, whose off stump was knocked out of the ground.
Hamilton then bowled Ben Hollioake to complete a career-best match haul of 11 for 72 before the innings ended with Saqlain Mushtaq miscueing a drive off Silverwood.
Earlier, as Yorkshire chose to bat on for 30 minutes before David Byas declared, White had completed his first century for more than a year. In the process the former England all-rounder, playing as a batsman because of a long-term back injury, hammered Bicknell over extra cover for the second six of his four-hour innings, which also included 12 fours.
Bradley Parker got in on this closing flurry of runs by clubbing six off Adam Hollioake while scoring a brisk 20 off 22 balls.Reuse content