A century from Sri Lanka maestro Kumar Sangakkara moved Surrey a step closer to the Division Two title.
Lancashire added 131 with their final five wickets to reach 272 all out, with 65 shared by last-wicket pair Simon Kerrigan and James Anderson (42).
Seventeen-year-old Sam Curran took a career-best 5-67 but Surrey chose not to enforce the follow-on.
Sangakkara, 37, struck his 54th first-class hundred as Surrey set a target of 492, with Lancashire closing on 22-0.
Surrey began the penultimate game of the campaign five points ahead of the Lancastrians and victory at Old Trafford would ensure them of the title before their final match against Northants at The Oval next week.
After his brother, Tom, had taken the vital wicket of Ashwell Prince, caught by first slip Sangakkara for 45 in the fifth over of the day, the younger Curran, a left-arm seamer, removed Jordan Clark leg before for 29 and yorked Tom Bailey first ball to collect the second five-wicket haul of his career.
Building on a first-innings lead of 208, Surrey quickly compiled 283-7 with Sangakkara, who retired from international cricket last month as the fifth highest run-scorer in Test history, reaching his fourth Championship hundred of the season in 115 balls, featuring 13 boundaries.
He hit two more fours before he was caught and bowled for 118, the sixth wicket to fall, and Surrey had seven overs at the Lancashire openers, who kept out the Curran brothers.
“I think we’re in a pretty strong position 470 ahead, Sammy with his five-for and Sanga batted beautifully.
“Sam was the Curran to to get the wickets today but the way TC [Tom] bowled, the channels and more importantly the length he bowled was pretty outstanding.
“It took Sanga about 15 balls to get going, I was out there with him and he was finding it a bit hard to time it, but then a typical Sangakkara stroke through the covers and he kicked into another tempo.
“It can be quite attritional at times, wickets have fallen in clusters. There is some spin there, which is good for Batts [skipper Gareth Batty]. For the seamers it’s about being consistent, we’ve done that really well with the length we’ve bowled and hopefully we can replicate that.” (Courtesy BBC Sport)