Buoyant after successive away victories at Derby County and Leeds United, Keane had to rely on an astute substitution midway through the second half to rescue a point.
Within a minute of replacing a subdued Liam Miller, left winger Tobias Hysen scored a superb 64th minute equaliser to cancel out Matt Fryatt's first goal of the season in the 48th minute.
Although the Black Cats were without injured strikers David Connolly, Stephen Elliott and Jonathan Stead, Keane's former Manchester United team-mate Dwight Yorke had to be content with a place on the substitute's bench following his £200,000 transfer from Australian club Sydney FC.
But the newcomer waited only 14 minutes to make his Championship debut, replacing the injured Daryl Murphy as the home side's injury jinx continued.
Leicester, however, looked the more likely to score as their neat approach play caused several anxious moments to an often hesitant defence well-marshalled by Stan Varga on his return to the Stadium of Light.
Levi Porter drove just wide and Stephen Hughes headed over after Neill Collins had scrambled the ball behind for a corner.
Sunderland replied with a diving header from Chris Brown that flashed just wide and then goalkeeper Paul Henderson made a fabulous save from Varga's well-struck volley.
A shrewd pass from Yorke set up the chance for Ross Wallace to hit a fierce drive across the face of goal but the visitors continued to enjoy the better of the first-half exchanges with Ben Alnwick just beating Fryatt to a low centre from the enterprising Porter.
A crisp volley from Porter struck Collins on its way behind and, from the corner kick, Patrick McCarthy headed over when well-placed. Fryatt was brought down just outside the penalty area but the home side survived.
But Keane's side were shell-shocked three minutes into the second half when the Foxes deservedly went ahead. Miller lost possession and Andy Johnson slipped the ball through the legs of Varga for Fryatt to cut inside Collins and easily beat Alnwick with a low shot into the corner of the net.
And it should have been even worse for the home side in the 53rd minute when the unmarked McCarthy headed over from a left-wing corner with the goal at his mercy.
Leicester were made to pay for the miss following a last throw of the dice by hauling off Miller and sending on Hysen, the Swede racing clear to send a low 20-yard drive into the bottom corner.
Brown headed over a Miller free-kick as the Black Cats stepped up a gear but with Leicester always dangerous on the break, a point apiece was a fair result.