John Scales' first half header and a strike by Robbie Fowler six minutes from time gave Liverpool the advantage over first division Burnley.
But the visitors defended stoutly and attacked with passion, and Liverpool boss Roy Evans will not be underestimating the task his side will face at Turf Moor.
The opening goal came after 42 finely balanced minutes, Steve McManaman's corner finding Jamie Redknapp, whose high cross was headed powerfully home by 3 million pound former Wimbledon centre half Scales to give him his first goal for his new club.
But their lead for the second leg looked like being a slender one until Jamie Redknapp and Stig Inge Bjornebye combined to set Fowler up for a precise low drive that flew just inside the post after 84 minutes.
Liverpool looked businesslike in the first half, carving out some useful chances. A deft through ball by John Barnes to Ian Rush after seven minutes saw the Welsh international striker sprint to the by-line before pulling the ball back for Fowler, who was denied by a fine last ditch challenge from Steve Davis.
Jan Molby fired wide with 'keeper Marlon Beresford stranded out of his goal after clearing from a right flank raid by Steve McManaman and Rob Jones, and Molby's next shot was thwarted by a good save from Beresford after 19 minutes.
Scales was unlucky to see a close range snap-shot bounce off Mark Winstanley's foot, and a slick 40th minute link-up between Molby and Rush saw Beresford go down bravely to save at the feet of McManaman.
But Liverpool had it far from all their own with Burnley matching them for enterprise, pace and endeavour.
The first division outfit carved out the game's first real chance after five minutes when Gerry Harrison played a one-two with David Eyres and curled a shot a couple of yards wide.
Ex-Everton striker Adrian Heath headed over the bar from an Eyres free kick after 17 minutes and soon after Harrison's 20-yard drive was beaten down by 'keeper David James.
On the half hour Heath flicked on Ted McMinn's right wing centre but James rescued Liverpool with an instinctive one-handed parry.
Alan Harper almost snatched an equaliser with a low angled shot that just beat the far post six minutes after the break, following a careless defensive clearance.
Liverpool were finding chances harder to come by after the break, falling for Burnley's offside trap in a number of promising situations.
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