Leeds bounced back from their embarrassing FA Cup defeat by Oxford as Liverpool slipped to their second defeat in a week.
Goals by David Wetherall in the 10th minute and skipper Gary McAllister three minutes from the end left Liverpool still waiting for their first victory since manager Roy Evans replaced Graeme Souness.
Evans dropped Nigel Clough, Mark Walters and Steve Nicol, bringing in Dominic Matteo, Neil Ruddock and Jamie Redknapp, but Liverpool continued to look vulnerable in defence, with Rod Wallace's pace causing them problems.
Bruce Grobbelaar showed the best and worst aspects of his goalkeeping. He was at fault for Leeds' first goal when he carelessly punched McAllister's free-kick straight to Wetherall, who punished the error with a deadly low shot.
Then, 19 minutes into the second half, the colourful Zimbabwean international allowed McAllister's 22-yard drive to slip through his hands and hit the bar.
But Grobbelaar was at his best in diving across his line to save a stunning 12-yard volley from substitute David White, who had been on the field less than a minute after replacing the injured Wallace.
Grobbelaar's super save was only bettered by an astonishing effort from Leeds' recalled 'keeper John Lukic, who denied John Barnes an equaliser three minutes after the interval when he met Ronnie Whelan's cross inside the six yard area.
Leeds' Republic of Ireland defender David O'Leary had a solid game on his return to Premiership football after a six-month injury absence.
Rush is happy to stay with Liverpool despite reports that he is interesting other clubs.
The Welsh international revealed after his team's 2-0 defeat at Leeds: "I was told two offers had been made for me and I said if Liverpool wanted me to go I would talk to both clubs. But they want me to stay, so I will remain with them for as long as they want me."
Manchester City's interest was confirmed by Liverpool's new manager Roy Evans who commented: "He told me he didn't want to go anywhere and that delighted all of us."
Evans refused to make excuses for Liverpool's second defeat in a week. He said: "We have got to the stage where we can't say we're unlucky. We just can't put the ball in the net. I think we need additions in several positions."
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