Sam Byram had put the visitors in front soon after the interval with his third goal of the season, but they were denied by Keane in stoppage time.
The Foxes defender nodded in Martyn Waghorn's 93rd-minute corner at the far post when it seemed play-off chasing Leeds had clinched their third win in four matches.
Leeds, who had not won on their travels in the league since victory at Huddersfield on December 1, were grateful to goalkeeper Paddy Kenny, who saved brilliantly from Anthony Knockaert and Harry Kane in the first half.
But Neil Warnock's side carved out as many chances as Leicester, for whom Kasper Schmeichel was also in fine form against his former club and whose own promotion hopes had suffered a setback following Saturday's defeat at Ipswich.
Leicester midfielder Knockaert fired the game's first chance over the crossbar from inside the penalty area after 37 seconds and home striker Chris Wood lifted his shot over from even closer nine minutes later.
Leeds responded and almost opened the scoring when they launched their first attack, left-back Stephen Warnock crossing for right-back Byram, whose goalbound header was parried by Leicester goalkeeper Schmeichel at full stretch.
Leeds midfielder David Norris and Wood traded long-range shots that were held by Schmeichel and visiting keeper Kenny respectively before Kane, on loan from Tottenham, forced the latter into a fine save with a raking 25-yard effort.
Teenager Kane, making his third appearance since arriving at the end of last month, was prominent for the home side. He lashed another 25-yard shot wide and Kenny pulled off another smart save to turn away Wood's curling effort 10 minutes before the break.
Leeds had soaked up considerable pressure, but broke away to threaten Schmeichel's goal again when Byram's clever cutback in the area was drilled wide, before another superb Kenny save kept out Knockaert's free-kick after former foxes defender Lee Peltier had fouled Wood.
But it was Leeds who broke the deadlock seven minutes into the second half.
Ross McCormack swung over a corner from the left and when the ball broke loose six yards from goal, Byram tucked it home into the bottom corner.
Leicester were then dealt another blow when defender Paul Konchesky was forced off injured and replaced by Lloyd Dyer and Schmeichel was at his alert best soon after when saving McCormack's bullet from 25 yards with his feet.
Foxes boss Pearson sent on winger Ben Marshall for Knockaert on the hour-mark, but both sides found goalscoring chances hard to come by in the final quarter.
Wood's driven effort in the box rebounded back off team-mate David Nugent in the 79th minute and Kane was off target from the edge of the area, but deep in time added on Keane rose at the far post to power home Waghorn's corner.