In the final Premier League fixture of 2012, Rodgers was not at Loftus Road due to a virus and the visitors from Merseyside were instead led by first-team coaches Colin Pascoe and Mike Marsh.
But the nonattendance of their manager did little to hurt Liverpool, who bounced back from the Boxing Day defeat by Stoke City with a double from the superb Luiz Suarez and a Daniel Agger header in the first half.
QPR, meanwhile, head in to 2013 seemingly needing a miracle to escape relegation after Harry Redknapp saw his team at times torn to shreds by their opponents' waves of attacks in London.
Liverpool started much the better team and their superior passing soon led to the opening goal as Suarez turned Clint Hill outside the box before advancing into the penalty area and firing past Julio Cesar after just 10 minutes.
Uruguay international Suarez was running the QPR defence ragged and, only six minutes later, he doubled the score when finishing from close range after his initial cross-shot had been blocked straight back to his feet by Nedum Onuoha.
Redknapp's rock-bottom Premier League hosts were getting ripped apart by attack after attack from Liverpool and, with a sense of inevitability, Agger made it 3-0 in the 28th minute with fine header from Steven Gerrard's right-wing cross.
Liverpool continued their onslaught and captain Gerrard was unfortunate not to add a fourth before half-time when his 18-yard effort ricocheted off several QPR defenders before somehow failing to cross the goalline.
Redknapp stood shaking his head on the touchline, having started the game already at the foot of the table and eight points adrift of safety, and he heard his team, still with just one league win this season, booed off at the interval.
QPR replaced former Liverpool striker Djibril Cisse with Shaun Derry for the second half and they improved, clinging to the hope of a repeat of last season's comeback against the same opponents, who blew a two-goal lead to lose 3-2 in London in March.
But Cesar was still busy to prevent Suarez from completing his hat-trick with an 18-yard shot, Onuoha just beat Gerrard to what would have been a goalscoring header and Jordan Henderson blazed over when well placed.
Liverpool's afternoon was only soured when losing left-back Jose Enrique to an apparent hamstring injury in the latter stages before the final whistle.