Second-half strikes from Liverpool's terrible twosome of Steven Gerrard and Fernando Torres took the Anfield men five points clear of local rivals Everton in fourth spot.
Gerrard scored his 21st goal of the season after a fine passing move on the hour, and the Liverpool skipper then created Torres' 30th of the season with eight minutes left.
The pair have now passed 50 between them for the season, with substitute Andriy Voronin adding the third before Roque Santa Cruz netted for Rovers, both in the final seconds.
It leaves Rovers facing an almost impossible task in their quest for the final European place.
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