Brown axed five players from the team which lost 4-0 at MK Dons last Sunday and switched to a five-man defence.
The tactic appeared to take Posh by surprise and United were second best from the start.
Lincoln went close after 11 minutes when Jamie Hand broke from midfield and fired in a shot which squirmed through the grasp of Mark Tyler.
Louis Dodds moved in for the kill but Tyler recovered to grab the ball at the second attempt.
Peterborough escaped again in the 20th minute when Nat Brown set up Lee Beevers but the centre-back headed wide from two yards.
Eight minutes later Peterborough were reeling again when Gary Croft sent a ball in from the left but both Ben Wright and Lee Frecklington were inches away from making contact.
The Red Imps deservedly went in front on the stroke of half-time when United failed to clear a corner from Scott Kerr.
Adie Moses headed against the bar before Wright followed up to sweep the ball home from inside the six-yard box.
Peterborough improved in the second half and went close when Charlie Lee broke clear and saw his shot saved at point-blank range by Alan Marriott.
But Lincoln should have scored a second in the 54th minute when Dodds got away. His first shot was blocked by the legs of Tyler but he beat the keeper with his follow-up effort only to see the ball come back off the bar.
Peterborough pushed men forward and were totally on top in the closing minutes. George Boyd saw an effort deflected over the bar and then Charlie Lee shot wide.
A minute from time ex-Lincoln man, Dean Keates, beat Marriott from 30 yards but was denied by the woodwork.
United kept up the pressure and substitute Rene Howe created the equaliser with an 89th-minute cross from the left.
Boyd tried to get there first but was beaten by Lincoln's Ollie Ryan who could only turn the ball into his own net for the equaliser.