Jamie Carragher moved to centre-back alongside Djimi Traore, while Salif Diao came on at right-back.
Jerzy Dudek also required treatment but was able to carry on.
Michael Owen put the Reds ahead on 31 minutes with his first goal from open play against David Moyes' side.
David Unsworth equalised from the penalty spot on the hour, but Danny Murphy scored what could be the goal of the season to give Liverpool the much-needed three points for their quest for Champions League football next season.
David Weir and Gary Naysmith were both sent off for Everton as their frustration started to show in the final ten minutes of the game.
With Chelsea losing at Aston Villa and Newcastle losing at Fulham this victory puts Houllier's men two points behind the Londoners and only three points behind third-placed Magpies.
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