But Gerrard was over-exuberant when he was booked for a late challenge on Smith after 27 minutes - and made a crucial error as Leeds doubled their advantage five minutes later.
Leeds United took a giant stride towards a Champions League slot via the Premiership next season with a crucial victory against Liverpool at Anfield.
David O'Leary's side - who are still in contention to win this season's European showpiece - moved menacingly into third place with an impressive display.
Leeds started in rampant mood and left Liverpool facing a massive task with first half goals from Rio Ferdinand and Lee Bowyer.
Steven Gerrard threw Liverpool a lifeline with a goal at the start of the second half - but was then sent off as Gerard Houllier's side slipped to a costly defeat.
It was a win that opens up a crucial six-point gap between Leeds and Liverpool in the scramble for Champions League places behind Manchester United and Arsenal.
Liverpool boss Houllier went with an attacking duo of Robbie Fowler and Michael Owen, resting Emile Heskey after he scored in successive games against Wycombe Wanderers and Ipswich Town.
Leeds were swiftly out of the blocks and swept into the lead in the fourth minute.
Liverpool were guilty of poor marking at Ian Harte's corner, allowing Ferdinand to steal in and head past Danny Murphy as he guarded the near post.
Murphy led the Liverpool response with a clever free-kick two minutes later, but Leeds goalkeeper Nigel Martyn was alert to the danger and saved splendidly.
Leeds were dominating affairs, with only Gerrard able to match the industry of O'Leary's buoyant side.
But Gerrard was over-exuberant when he was booked for a late challenge on Smith after 27 minutes - and made a crucial error as Leeds doubled their advantage five minutes later.
He gave the ball away to Dacourt, the opening half's outstanding figure, who found Harry Kewell racing into the Liverpool danger area.
Kewell played a clever pass through to Bowyer, who scored at the second attempt after Liverpool goalkeeper Sander Westerveld blocked his first effort.
Liverpool boss Houllier had to make changes to lift his struggling side - and used the half-time interval to replace Murphy and Patrik Berger with Vladimir Smicer and Gary McAllister.
Jamie Carragher found Owen on the right hand flank, and he picked out Gerrard perfectly at the far post to give Liverpool renewed hope.
Liverpool suddenly found all the passion and pace that had deserted them in the opening half.
And Leeds defender Danny Mills followed Anfield pair Smicer and Dietmar Hamann into referee Alan Wiley's notebook as the tackles flew in.
Houllier played his final card after 65 minutes, replacing Hamann with Heskey.
But Liverpool suffered a blow four minutes later Gerrard's timing and judgement let him down and he was shown the red card.
Referee Wiley had no option other than to show the red card when Gerrard upended David Batty in a midfield tussle.
Leeds almost took instant advantage when Mark Viduka burst forward and deceived Sami Hyypia, only to see his shot bounce off the outside of an upright.
And Viduka was denied another opportunity to effectively seal the game after 76 minutes when he allowed Westerveld to plunge at his feet to make a crucial save.
The giant Aussie had a goal ruled out for offside as Leeds hit Liverpool on the break.
It was a close decision, which looked harsh against the Leeds striker, but did not prove costly as O'Leary's side held out in relative comfort.
Liverpool: Westerveld, Babbel, Henchoz, Hyypia, Carragher, Gerrard, Murphy, Hamann, Berger, Fowler, Owen. Subs: Smicer, Heskey, Arphexad, McAllister, Vignal.
Leeds: Martyn, Mills, Matteo, Ferdinand, Harte, Bowyer, Dacourt, Batty, Kewell, Viduka, Smith. Subs: Kelly, Keane, Robinson, Wilcox, Bakke.
Referee: A Wiley (Burntwood)