This FA Cup fourth round tie was in stark contrast to the goalfest last year as the ensuing stalemate suggested that a replay would be required at Anfield.
However, substitutes Barmby and Heskey produced the goods in the closing stages to send the Worthington Cup finalists into the hat for the fifth round draw.
Barmby was the key figure, lashing home from a difficult angle to break the deadlock after 88 minutes. A sloppy pass from Ian Harte in midfield gifted a throw-in to Liverpool and, when Christian Ziege`s run was ended, Robbie Fowler instinctively prodded the ball goalwards.
It struck a post with the returning Nigel Martyn static in the middle of his goal, and Barmby was on the spot to ram the rebound into the net from the right hand side of the box.
With the away fans still celebrating, a second goal arrived deep into stoppage time when Fowler`s endeavour down the left flank allowed him to pick out Barmby at the far post.
This time the England international turned provider, teeing up Heskey to rap a barnstorming finish into the net, via the left hand of Martyn, who was unable to keep out the powerful drive.
The Leeds keeper did not make a single save of note in the game and yet he still finished on the losing side, Liverpool scoring with their only shots on target.
Lee Bowyer had a strong case for a penalty, which would have given the hosts a lifeline with the score at 0-1, when he appeared to be tripped inside the area by Gary McAllister but, to be fair to referee Andy D`Urso, the incident ocurred amongst a sea of legs.
The match got off to a sensational start when Bowyer`s excellent pass caught the Reds defence napping, allowing Robbie Keane to run in on goal. Sander Westerveld managed to get a heavy touch to the shot and it was cleared to safety by Stephane Henchoz on the line.
Liverpool, missing two of their most influential figures of late in Steven Gerrard and Jari Litmanen, struggled to impose themselves as Leeds called most of the shots in the opening half.
Although Westerveld was rarely called into action, Keane and Mark Viduka were the livelier of the two forward lines, and the Irishman should have done better when sprinting through, only to turn onto his left side and allow Henchoz to make a saving tackle. Viduka blasted the loose ball wide.
The most noteworthy incident of the first half was a flashpoint involving firebrand Bowyer and former Elland Road star McAllister.
The Leeds midfielder, due in court next week, flayed an elbow into the face of the Scot, who had earlier been booked for holding up a free kick.
Although McAllister needed treatment for a facial wound, referee D`Urso decided the contact was unintentional, and, probably wrongly, took no action against Bowyer.
Westerveld saved comfortably from Bowyer as Leeds threatened towards half time, and Keane had half-hearted penalty appeals rejected when he drilled a cross straight at Henchoz, but the visitors looked comfortable going into the break at 0-0.
Gerard Houllier`s men had more of a grip on the game, right from the restart, with Smicer mustering a couple of attempts from the edge of the area.
Viduka had a chance to score, evoking memories of one of his strikes in the 4-3 classic earlier in the season, but pulled his finish across the face of goal on this occasion.
Just before the hour mark, Westerveld almost gifted Leeds an opening goal when he inexplicably dropped a harmless looping header to the feet of Eirik Bakke. The Norwegian toe-poked the ball goalwards, but the Dutch keeper`s blushes were spared by Sami Hyypia, who thrashed it off the line.
McAllister, nudging a Murphy cross wide at the near post, and Fowler, wastefully dragging his finish into the side-netting after turning Jonathon Woodgate, went close for the Merseysiders, as both sides searched for a priceless goal.
Perhaps the clearest opportunity of the game fell to former Red Dominic Matteo when Bowyer`s far post cross cried out for a finishing touch. Unmarked and allowed a free header, he could only steer his header over the bar from a couple of yards out.
A number of substitutions threatened to ignite some much-needed spark into the proceedings, with Liverpool`s top scorer Emile Heskey and England colleague Barmby coming on for the visitors, and Alan Smith replacing the tiring Keane, who had flattered to deceive. Of course, it was the visiting duo who were to have the major impact.
An injury to Danny Murphy, who had looked inventive in midfield, will be a concern to Houllier, with Ziege forced into action to replace the former Crewe man, but he will be delighted with the result.
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