Smith had called for his team-mates to show more fighting spirit and he set the perfect example.
Mark Viduka maintained his late season scoring spree, but foolishly earned a second yellow card for booting the ball away in injury time and was sent off.
He will miss Leeds' vital home match against Portsmouth on Sunday April 25.
Michael Duberry celebrated his recall by heading the first Leeds goal, but Leicester roared back with second-half goals by substitute Paul Dickov and skipper Muzzy Izzet.
This was the game neither side dare lose in the scramble for Premiership survival and Leeds could hardly have made a better start with goals in the 11th and 13th minutes.
First, Seth Johnson's inswinging corner to the near post was cleared to Gary Kelly outside the box. He fed Johnson whose perfect cross was headed powerfully home by Duberry from seven yards out.
Two minutes later Smith miskicked inside the box and Viduka reacted quickly with an inventive overhead shot from eight yards for his fifth goal in his last six outings.
Eddie Gray's decision to give his midfield more steel by moving skipper Dominic Matteo from the back in place of the unlucky Stephen McPhail paid off, while Duberry, fit again after seven matches out with a rib injury, relished his comeback.
Leicester had four specialist strikers on the pitch when Dickov replaced Steve Guppy seven minutes before the break in a bid to retrieve the situation.
Jermaine Pennant had a penalty claim rejected when he appeared to be elbowed by Nikos Dabizas just before half-time.
Ian Walker pulled off two miraculous second-half saves to prevent Smith adding to Leeds' tally before Leicester grabbed two goals in three dramatic minutes to pull themselves level.
Dickov took a pass from Marcus Bent to shoot past Paul Robinson's right shoulder in the 76th minute and Izzet then stunned the Leeds faithfull into silence by beating Robinson from 25-yards.
But the drama wasn't over as Smith grabbed Leeds' 87th minute winner, driving home after combining excellently with James Milner and Viduka.
Aussie Viduka was then ordered off, meaning he misses the crucial game against Pompey, but Leeds held out for three precious points.
A win at Blackburn on Saturday and we'll be on level terms with them.