After a scrappy, goalless first half the Reds started the second 45 better and Sebastian Coates, on for the injured Martin Kelly, scored on 53 mins.
Liverpool then piled on the pressure and scored a second, Dirk Kuyt netting from a rebound after Jordan Henderson shot following good work from Luis Suarez.
But QPR weren't giving up the fight. Jamie Mackie came on for Joey Barton and gave the home side the lift they needed. Shaun Derry got one goal back on 75 mins, former Liverpool frontman Djibril Cisse equalised with five minutes remaining and Mackie netted the winner in stoppage time.