Super-sub Bruno Fernandes' fantastic free kick secured Manchester United's 3-2 FA Cup fourth-round victory over bitter rivals Liverpool as Ole Gunnar Solskjaer enjoyed his first triumph against Jurgen Klopp's men.
Earlier on Sunday, Chelsea striker Tammy Abraham grabbed a hat-trick in a 3-1 win over Championship side Luton Town at a snowy Stamford Bridge to also book their place in the fifth round.
Top-flight sides Leicester City, who came back from a goal down to beat second-tier Brentford 3-1, and Burnley, who were grateful for Jay Rodriguez's double in a 3-0 win at Fulham, also progressed.
Everton dispatched Sheffield Wednesday by the same score at Goodison Park thanks to Dominic Calvert-Lewin, Richarlison and Yerry Mina goals.
A week on from a tense goalless draw at Anfield between the Premier League leaders and reigning champions, all eyes were on Old Trafford as United's home hosted a far more entertaining encounter between these old foes.
Mohamed Salah's fine opener was cancelled out by Mason Greenwood in an entertaining first half.
Marcus Rashford coolly then put United ahead after the break only for Salah to level with his second, setting up a grandstand finish in which star man Fernandes came off the bench to score a superb free kick winner, his 28th goal for United since his debut last February.
"When you leave him out like I did today, he stayed about 45 minutes after training yesterday shooting free kicks so I was pretty confident he could score one if he got the chance," United boss Ole Gunnar Solskjaer, whose side have lost only once since exiting the Champions League in early December, said.
A home clash against West Ham is the reward for United, who Solskjaer led to victory against Liverpool at the fifth time of asking - 22 years to the day after he scored the winner against them at the same stage of the competition.
Defeat made this the fifth time in six seasons that the Reds had failed to progress beyond the fourth round under Klopp.
At Stamford Bridge, Abraham scored his first Chelsea hat-trick, netting in the 11th, 17th and 74th minutes.
"Great to score a hat-trick and win the game so comfortably," Abraham said.
"It is always nice to get a win and play well. Hopefully we will take that confidence on."
Leicester, who were without striker Jamie Vardy due to a hernia, were stunned in the seventh minute when Danish defender Mads Sorensen put Brentford ahead.
But second-half goals from Cengiz Under, Youri Tielemans, from the penalty spot, and James Maddison saw the Foxes through to face Brighton & Hove Albion in an all-Premier League tie.
Rodriguez's double, plus a goal from Kevin Long, earned Burnley a meeting with either fourth-tier League Two side Crawley Town or Bournemouth.
DRAW FOR THE FA CUP FIFTH ROUND
Manchester United v West Ham United
Barnsley v Chelsea
Swansea City v Manchester City
Wolverhampton Wanderers v Southampton
Sheffield United v Bristol City
Leicester City v Brighton & Hove Albion
Burnley v Bournemouth or Crawley Town
Everton v Wycombe Wanderers or Tottenham Hotspur.
Australian Associated Press