The Uruguay international, who has been in the headlines for the wrong reasons during a two-month lean spell in front of goal, was at his threatening best as he scored his first goal in the Premier League since October 1.
His header ended a run of four successive draws at Anfield and helped repair some of the damage done to his reputation in recent weeks.
Suarez had been the main topic of conversation pre-match - having received his second Football Association misconduct charge of the season earlier in week for allegedly making an offensive gesture to Fulham fans - but it was another instrumental display on the field which was the talking point afterwards.
The 24-year-old has found himself targeted by opposition players and fans alike who believe the South American goes to ground far too easily.
Early signs at Anfield were that QPR were not going to dish out the sort of harsh treatment that had prompted Reds manager Kenny Dalglish to produce video clips in a determined defence of his striker at his press conference on Thursday.
Suarez, who is also facing a racism-related charge dating back to mid-October, should have taken advantage in the 10th minute from Stewart Downing's right-wing cross but he headed straight at Radek Cerny from 10 yards.
It set the tone for the rest of the half as he then somehow squeezed a shot from a narrow angle between the goalkeeper and his left-hand post which eventually went out for a throw before skewing wide with the outside of his right foot when it looked easier to go with his left.
Having dominated at home against the other promoted teams Norwich and Swansea - which both finished in draws after missing a number of chances - a familiar pattern was developing for Liverpool.
In the 31st minute Dirk Kuyt put Maxi Rodriguez through in the inside-left channel and his low shot across Cerny was destined for the far corner of the net until the goalkeeper fingertipped it behind.
A driving run from Downing set up another Suarez chance but his attempted close-range lob was clawed away by Cerny and the Uruguay international blazed over the rebound.
It took Liverpool just two minutes to put the frustrations of the first half behind them when they returned after the interval.
Charlie Adam's left-wing corner was cleared back to him and his right-footed cross picked out the unmarked Suarez who easily headed past Cerny from five yards.
It was the Uruguayan's first goal since getting two in the Carling Cup in late October and his first in the Premier League since the Merseyside derby on October 1.
The situation worsened for QPR when Anton Ferdinand sustained a hamstring injury and had to be replaced by Bradley Orr.
Suarez continued to be Liverpool's main threat in the final third and when he pulled the ball back for Rodriguez to shoot only a great one-handed save low to his left by Cerny prevented a second all-important goal.
Rodriguez should have scored after a brilliant interchange with Suarez in the area but he wastefully shot straight at the goalkeeper.
Liverpool continued to dominate but QPR were always capable of nicking a goal and they almost did when Danny Gabbidon, five yards out, diverted over Joey Barton's inswinging free-kick.
Neil Warnock's side enjoyed their best spell in the closing 20 minutes but the hosts still looked the most likely to score again as substitute Craig Bellamy curled a free-kick into the side-netting.
QPR felt they should have had a penalty late on when Alejandro Faurlin went down under Martin Skrtel's challenge but referee Lee Mason saw nothing wrong.
In the last action of the game Shaun Wright-Phillips deflected Bellamy's cross on to the bar but, unlike in recent weeks, one goal proved to be enough as Liverpool moved up to sixth in the table.