Strauss, who made a third-ball nought as Middlesex were skittled out for just 98 in their first innings, made 117 not out.
It was much-needed innings by Middlesex from their former captain after Hampshire, showing the much-maligned Rose Bowl pitch was not the prime cause of the Londoners' initial downfall had piled up 426, including an innings of exactly 100 from wicket-keeper Nic Pothas.
Strauss's 175-ball innings featured 17 fours but at 204 for three at stumps on the second day, Middlesex were still 124 behind.
At Headingley there were no night-watchman heroics from Jason Gillespie. Fresh from his double century against Bangladesh, the Australia fast bowler went third ball as Yorkshire finished the day on three for two in their second innings against Sussex.
Earlier the visitors built a 29-run lead on the back of Matt Prior's 124. Yorkshire and England seamer Matthew Hoggard took three wickets.
Also taking a treble was England pace hopeful Sajid Mahmood, widely tipped to be in the squad due to be announced Sunday for the first Test of three against Sri Lanka at Lord's
Lancashire captain Mark Chilton made 118 not out as the hosts reached 293 for three at Old Trafford in reply to Kent's 327.
Reigning champions Nottinghamshire were bowled out for a mere 157 in reply to Warwickshire's 248, with veteran seamer Dougie Brown taking four for 49 for the visitors at Trent Bridge.
At stumps Warwickshire were 187 for three in their second innings, a lead of 278, with England batsman Ian Bell 72 not out.
In the second division, former England batsman Mark Ramprakash scored an unbeaten 276 as Surrey piled up a huge 608 for seven in reply to Gloucestershire 207 at The Oval.
The 11th double century of Ramprakash's career has so far featured one six and 32 fours in 403 balls.
A century on championship debut for Glamorgan's South Australian batsman Mark Cosgrove was the highlight at Sophia Gardens, where the mid-match balance of power was evenly contested.
Cosgrove's run-a-ball 114 contained 23 fours and one six - while his third-wicket partner Michael Powell contributed a more solid 100 to help the Welsh county to 296 for six in response to Derbyshire's 335.
Hundreds from South African all-rounder Lance Klusener (147no) and Bilal Shafayat put Northamptonshire in charge against Somerset.
The hosts made 449 in reply to Somerset's 258 featuring a hundred from England opener Marcus Trescothick.
Somerset's Australian off-spinner Dan Cullen bowled 43 overs for his five for 137.
Klusener hit one six and 22 fours in just 184 deliveries.