Lincoln City 1 Milton Keynes Dons FC 1
Baker flung himself to his right to push out a downward header from Lincoln striker Marvin Robinson which looked a certain winner.
But that would have been hard luck for the Dons who fully deserved a replay after a hard-fought cup clash.
Lincoln were on top early on with winger Derek Asamoah caught tormenting the Dons' defence. He set up a half chance for Robinson in the first minute but the striker shot wide.
Asamoah then beat two defenders but hit a left foot shot narrowly wide.
Asamoah was in the thick of things again in the 11th minute when he got on the end of a Nat Brown header but shot against the body of Baker.
Colin Cryan went close 60 seconds later when his first time shot was blocked on the line by Trent McClenahan.
The Dons escaped again in the 20th minute when Lincoln midfielder Dean Keates hit a free-kick over the defensive wall and against the post.
But Lincoln finally went in front nine minutes later. Cryan sent a perfect cross into the box and Robinson dived forward to head home from ten yards.
Lincoln then eased off and let the Dons back into it. The visitors drew level in first half stoppage time when a long range shot from Gareth Edds took a deflection and finished up in the back of the net.
Dons almost scored again in the 57th minute following more good work by Edds. The midfielder produced an excellent cross which found the head of Clive Platt but his header was blocked on the line by Lee Beevers.
Lincoln tried to get a late winner but Gary Birch, making his come back from injury, headed wide from close in.
Lincoln were reduced to ten men in stoppage time when Keates was red carded for a challenge which left Dons substitute Gary Smith needing treatment.