Fast bowler Tremlett took six for 42, surpassing his five for 87 against Australia in Perth in December.
The 29-year-old giant quick ripped through Sri Lanka's middle and lower order with four wickets for 16 runs in 32 balls here on Friday.
Nevertheless Sri Lanka's total represented something of a revival from the depths of 39 for four.
Dilhara Fernando was 33 not out and Chanaka Welegedara seven not out when the players came off the field.
Tremlett, who made his name at the Rose Bowl with southern county Hampshire before moving to Surrey last season, had helped bowl England to an innings and 14-run first Test win in Cardiff before the drawn second Test at Lord's.
In this match, he'd already exploited the assistance offered by a green-tinged pitch to take two for 17 in 11 overs on Thursday before Thilan Samaraweera and Prasanna Jayawardene kept England at bay.
But, after rain meant no play before lunch on Friday, Samaraweera could only add seven to his overnight 24 before he was dismissed in Tremlett's first over of the day.
The 6ft 7in quick struck Samaraweera a painful blow on the glove with his second ball Friday and, four deliveries later, induced a loose drive straight to Kevin Pietersen in the gully to end a stand worth exactly fifty.
Tremlett then had recalled all-rounder Thisara Perera out edging an intended pull through to wicketkeeper Matt Prior.
Sri Lanka were now 91 for six, with Tremlett having taken two wickets for two runs in seven balls.
The one consolation for the tourists was they'd at least managed more runs than their record low Test score in Britain of 82 all out in Cardiff.
Tremlett though completed his five-wicket haul when Rangana Herath top-edged a pull to James Anderson at fine leg to leave Sri Lanka floundering at 117 for seven.
But, after Tremlett's spell of three for 18 in six overs, Stuart Broad was unable to follow-up, the seam-bowling all-rounder too often harmlessly short.
Prasanna Jayawardene, who made a century in the first Test, repelled England's attack with several stylish shots on his way to 43.
But England captain Andrew Strauss saw his move in bringing on Graeme Swann
vindicated by just the off-spinner's second ball, which Prasanna Jayawardene slog-swept straight to Eoin Morgan at deep midwicket.
Prasanna Jayawardene, in for nearly three hours, helped Fernando add 41 for the eighth wicket -- runs that could yet prove valuable -- before Tremlett's first ball back saw Suranga Lakmal caught behind for a duck.
