First the all-rounder took his Championship wicket tally for the season to 26 by helping to clean up the Durham tail as the visitors were bowled out for 384 from an overnight 353 for eight.
Then Trego hit his first half-century of the season, sharing a seventh-wicket stand of 99 with 18-year-old Craig Overton, who hit 50 off just 54 balls, before finishing unbeaten on 67.
Nick Compton scored 64 to move within 67 runs of 1,000 in first-class cricket this season, while James Hildreth smacked 53 from 39 balls with 10 fours and a six.
Centurion Ashwell Prince and Steven Croft underpinned a commanding display with the bat as
Prince and Croft shared a grafting fourth-wicket stand of 176 inside 61 overs to help their side recover from 55 for three during the morning session to close on 276 for four from 96 overs.
Prince, who notched his 32nd hundred in first-class cricket and his third in the Championship for Lancashire after spells in 2009 and 2010, finished the day unbeaten on 121 off 224 balls while Croft added 78 off 195.
Chris Wright took three for 42 and Keith Barker and Chris Woakes claimed two wickets apiece as no Surrey batsman reached 40.
The Bears replied with 106 for one, with Varun Chopra 59 not out.
Division Two leaders
The leaders were 37 for one in reply, Paul Borrington the man out for three.
With second-placed Yorkshire not in action, Kent had the chance to put the pressure on and rose to the occasion, skittling
The in-form Matt Coles took five for 41 as only Wayne White (38) and Ned Eckersley (31no) offered any resistance, with a seventh-wicket stand of 56.
Brendon Nash ended the day unbeaten on 50 as Kent reached 104 for two in reply.
Makeshift opener James Middlebrook scored a century as
The spinner made 121 and Kyle Coetzer added an unbeaten 81, with the pair putting on 134 for the second wicket.
Sean Ervine was 109no as
The Welsh side's reply stood at 13 without loss at stumps.