Carlisle had been on course for a shock first win in seven when journeyman Michael Bridges gave them a first-half lead but Foxes skipper Matt Oakley slotted home an equaliser.
Leicester looked to have snatched the three points necessary to keep them four points clear thanks to Matt Fryatt's 24th goal of the season but Dobie struck two minutes into injury-time to earn the Cumbrians share the spoils.
United had goalkeeper Ben Williams to thank for keeping the score goalless as he denied Max-Alain Gradel and Andy King with a superb double save, before tipping Fryatt's header round a post.
Carlisle took advantage when David Raven set up Bridges to slot home his fifth goal of the season from inside the area after 31 minutes, only for the leaders to pull level after 52 minutes when Lloyd Dyer's cross found Oakley, who made no mistake in finding the net from 12 yards.
Dyer then struck wide following a Fryatt cross before the pair exchanged roles as Fryatt headed home from the winger's assist. But in a bitter late twist for Leicester Michael Liddle provided the cross for Dobie to head past Tony Warner.