Blackburn goalkeeper Brad Friedel had a standout match against his former club -- with repeated strong saves from Michael Owen, Steven Gerrard and Emile Heskey.
"It was a dramatic start to the game and a deserved victory -- we played very well. If Michael Owen had been clinical it would have been 6-1 or 7-1, I said to Brad Friedel at the end that he kept them in it for a long time," Houllier said.
Duncan Ferguson scored the equalizer with two minutes left as Everton drew 2-2 with Newcastle, a match in which both sides finished with 10 men.
The Magpies had Laurent Robert sent off in the 40th minute for a second yellow card. Everton went down to ten men in the 58th minute when Gary Naysmith was shown a straight red card.
Alan Shearer scored both Newcastle's goals from penalties, sandwiched by Tomasz Radzinski's Everton goal in the 67th minute. Ferguson leveled with a penalty.
"Alan was the man of the moment, you need to be ice cool in a situation like that. He had two penalties in a cauldron and scored them both with great calmness," Newcastle manager Bobby Robson said.
Bruno N'Gotty and Kevin Davies scored as Bolton beat Middlesbrough 2-0 for its first win of the season, while James Beattie scored twice as Southampton beat bottom club Wolves 2-0.
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