On his penultimate appearance at Anfield, Gerrard missed the penalty that would have restored the hosts' lead after Leroy Fer's volley had cancelled out Philippe Coutinho's first-half goal.
But he showed a enduring knack for picking the moment when he pounced three minutes from time.
Defeat leaves QPR - who had Nedum Onouha sent off for two bookable offences within the space of four minutes, seven points from safety with just nine to play for and Manchester City up next.
Liverpool close the gap on Manchester United to four points in the race for Champions League qualification but some supporters made feelings known; a plane trailed a 'Rodgers out, Rafa (Benitez) in' banner across Anfield before kick-off.
There was a sombre atmosphere around Anfield before kick-off, though, after the news of the death of QPR defender Rio Ferdinand’s wife, Rebecca, and Liverpool paid their respects before the game as Gerrard handed Joey Barton a bouquet of flowers to pass onto Ferdinand.
The visitors, who wore black armbands, thought they had the lead just seconds into the game as Fer bundled home Matt Phillips’ corner, only to the see the linesman flag for a goal-kick after the ball went out of play.
It took Liverpool until the 16th minute to have their first attempt on goal and it was Rickie Lambert, making his first start in the Premier League since December 6th, who had it, cutting inside on his right foot before firing a shot straight at Green.
Despite QPR’s promising start, it was Liverpool who took the lead as Lambert picked out Coutinho with a pass from the right wing and the Brazilian took one touch, before curling the ball beyond Green and into the top corner (19).
Liverpool were finishing the half the stronger and they thought they should have had a penalty when Raheem Sterling’s cross appeared to hit Clint Hill’s arm, but referee Martin Atkinson remained unmoved.
Rodgers’ side had one final chance to double their advantage just before the break as Gerrard fired a free-kick goalwards but Green moved to his right well to make a smart save.
QPR boss Chris Ramsey was forced into a change at half-time with Yun Suk-young replacing the injured Steven Caulker, but it failed to stem Liverpool’s attacking threat. Adam Lallana was the first to go close as he dragged his shot wide before Sterling missed a glorious chance at the far post after Jordan Henderson’s brilliant cross.
The hosts looked like they had paid the price for not taking their chances when Fer's strike gave QPR hope of a point with 17 minutes remaining, but Gerrard eventually got them out of trouble.
The Liverpool skipper was handed his first chance to win the game in the 80th minute as Onuoha bundled Skrtel to the floor in the box, but, from 12 yards, Green was Gerrard’s nemesis again.
Minutes later, Onuoha - who was booked for the foul on Skrtel - received a second yellow card after a late challenge on Jordan Ibe, and with just three minutes remaining, Gerrard made up for his penalty miss to head home Coutinho’s corner.
Anfield rose as one as the 34-year-old was substituted soon after to hail another matchwinning performance, Liverpool still just in the hunt with three games remaining but QPR's fate at the other end all-but sealed.
Soccer Saturday verdict – Matt Le Tissier
“QPR were a little bit flat they started better and looked the sharper of the two teams in the opening exchanges. I was surprised when Leroy Fer got them back into the game but because they didn’t look like scoring in the second half. They didn’t threaten after that and it was no surprise when Liverpool got the winner.”