Surrey captain Burns was well supported by Ben Foakes, who hit a fine 82, as the Division One leaders and defending champions built a potentially match-winning halfway lead of 240 after bowling Lancashire out for 204 on day one.
In five balls' batting before bad light ruled out the last scheduled 7.1 overs of the day, Lancashire reached four without loss in their second innings.
Burns and Foakes put on 197 for the fourth wicket, with England's erstwhile Test wicketkeeper eventually out to the second new ball bowled through a weary-looking flip towards mid on by George Balderson's medium pace.
Former England opener Burns' 26th first-class hundred was his second of the season and his highest score since he made an unbeaten 219 against Hampshire at the Oval in 2017. He batted for seven and a half hours, facing 348 balls and hitting a six and 29 fours.
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