An early double for the Uruguayan and a header from Daniel Agger heaps misery on Harry Redknapp's side, who will go into 2013 rooted to the bottom of the Premier League table.
Suarez struck twice in the opening 20 minutes before Daniel Agger headed home from a corner in a dominant first half for Liverpool.
Reds boss Brendan Rodgers missed the trip through illness, so Colin Pascoe took charge, making three changes from Boxing Day's defeat to Stoke, while the most notable change in five for QPR saw Rob Green dropped in favor of Julio Cesar after his clanger in defeat to West Brom.
The Reds started brightly, and Suarez forced an early save from Cesar with a fierce drive that the Brazilian parried towards Joe Allen, but the Welshman scuffed his volley when following in.
Suarez was not to be denied in the 10th minute, though, as he picked the ball up 30 yards out and drove towards goal, leaving Clint Hill in his wake before calmly slotting home from inside the area.
Six minutes later, Liverpool and Suarez had a second as Stewart Downing released the Uruguayan down the right, where he lashed the ball across the box toward Raheem Sterling. Nedum Onuoha's last-ditch block put the ball back on Suarez's foot, and he swept it home from six yards.
Harry Redknapp's side was split open again soon after as Martin Skrtel's long ball from the back released Glen Johnson. The right back stormed at goal before scuffing across goal, beating Cesar, but Ryan Nelsen hacked away the danger with Suarez awaiting a tap-in.
The Hoops were undone again before the half hour as Downing's quick corner found Gerrard who swung a cross in that an unmarked Agger nodded back across goal and past Cesar at the vacant far post.
Redknapp responded at the break by replacing Djibril Cisse with Shaun Derry, but little changed as Sterling burst in from the left before feeding Suarez, whose stinging left-footed effort drew a flying save from Cesar.
The Reds' tempo dropped in the second period, with Reina being called into action by Adel Taarabt and Stephane Mbia, while substitute Esteban Granero scuffed a low free kick wide with his first touch.
The hosts ran out of steam late on, with only a tame Mbia free kick to show for their efforts as the game meandered to a close, as Liverpool climbed one place to ninth and ensured the Hoops will end 2012 rooted to the foot of the Premier League table.