Arsenal, thumped 5-1 in the Premier League by Liverpool last weekend, took sweet revenge at the Emirates on Sunday with a 2-1 win in the fifth round of the FA Cup.
Visiting manager Brendan Rodgers, however, was furious his side were denied a "blatant penalty" by 2010 World Cup final referee Howard Webb in the second half.
Arsenal will be at home again in the quarter-finals, having been drawn against Liverpool's local rivals Everton.
Arsene Wenger's team were in control when they led 2-0 shortly after halftime, Alex Oxlade-Chamberlain scoring the first goal after 16 minutes and then created the second for Lukas Podolski.
Podolski then conceded a penalty for a trip on Luis Suarez and it was converted by Liverpool captain Steven Gerrard in the 60th minute.
Liverpool felt they should have had another penalty for an Oxlade-Chamberlain challenge on Uruguayan Suarez soon after but Webb turned down their strong appeals.
"I thought it was a blatant penalty," Rodgers told BT Sport television. "Luis got a touch on the ball and young Alex has just taken him out."
Wenger was less certain that it was a spot kick. "Maybe, maybe not," said the Frenchman before adding: "I'm very proud of the way we responded to the huge defeat last week".
Earlier, Liverpool started the tie well but missed two early chances that fell to England striker Daniel Sturridge who had scored in his previous eight games.
Arsenal went ahead when a shot by French Under-21 international Yaya Sanogo, making his first start, fell kindly for Oxlade-Chamberlain to pounce.
Podolski made it 2-0 before Gerrard's penalty launched a Liverpool fightback.
Arsenal held on for victory, though, to gain a huge boost ahead of Wednesday's Champions League last-16 first leg at home to holders Bayern Munich.
Liverpool will now focus solely on the Premier League. Rodgers's men are in fourth place, four points behind leaders Chelsea.
Arsenal meet Everton in next month's quarter-finals after they beat Swansea City 3-1 at Goodison Park where Roberto Martinez stayed on course to become the first manager to win the FA Cup in successive seasons with different teams.
He led Wigan Athletic to victory over Manchester City in last season's final and those two sides will face each other again in the last eight after the draw was made on Sunday.
On Saturday, Manchester City beat league leaders Chelsea 2-0 while Wigan won 2-1 at Cardiff City.
Although Arsenal's victory meant there would be no all- Merseyside clash in the quarter-finals, there could be another derby after League One Sheffield United ended the 16-match unbeaten run of Championship side Nottingham Forest with a 3-1 win at Bramall Lane.
United will face Sheffield Wednesday in the competition for the first time since they met in the 1993 semi-finals if the latter eventually beat Charlton Athletic in a tie that was postponed on Saturday because of bad weather.
The other last-eight clash is between Sunderland, who ousted Southampton 1-0 on Saturday, and Brighton and Hove Albion or Hull City who meet on Monday.
The quarter-finals will be played on the weekend of March 8/9.