Juan Mata's excellent brace saw Manchester United to a 2-1 victory at Liverpool as substitute Steven Gerrard was shown a straight red card within seconds of his introduction.
United looked much the better team during the early stages, and they seized the advantage on 14 minutes when Ander Herrera's fine throughball found Mata, who fired a shot past Simon Mignolet and in off the post.
Liverpool might well have been level 10 minutes before the break when Daniel Sturridge's lay-off found Adam Lallana in space in the box, but the midfielder failed to hit the target.
Gerrard was introduced as a half-time substitute for Lallana, but he lasted less than a minute before being sent off for stamping on Ander Herrera.
The 10 men soon fell further behind as, just before the hour mark, Mata produced a scissor kick from Angel Di Maria's chip to send the ball into the far corner.
However, Liverpool still managed to claw their way back into the game when Daniel Sturridge managed to squeeze a shot past David De Gea at the near post.
Chelsea survived a major scare to secure a 3-2 win at Hull City and restore their six-point lead at the top of the Premier League.
Chelsea, who have a game in hand on second-placed Manchester City, had looked to be on course for a routine victory when Eden Hazard crashed home an opener inside two minutes and Diego Costa doubled their advantage with another impressive strike on 10 minutes.
However, there had been an early warning sign for the visitors when Abel Hernandez was denied by Thibaut Courtois after going clean through, and Ahmed Elmohamady was able to reduce the deficit when turning home Andrew Robertson's cross on 27 minutes.
Hull, who went into the game just three points clear of the relegation zone, found an equaliser moments later when Courtois' loose touch set up Hernandez for the simplest of finishes.
The home side then looked the more likely to force a winner, and Courtois was forced into an excellent triple save with 64 minutes on the clock, but Chelsea restored their advantage on 77 minutes when Loic Remy's shot somehow found its way past Allan McGregor.
Hull battled in search of an equaliser, and Hernandez looked to have a chance in the dying seconds, but Courtois claimed the ball and Chelsea left the KC Stadium with the three points.
Aaron Lennon scored his first goal for Everton to hand Roberto Martinez's side an important 2-1 victory at Queens Park Rangers.
Seamus Coleman opened the scoring for the Toffees in the 18th minute, though Eduardo Vargas found the net for QPR with 25 minutes remaining to set up a tense finale.
Coleman turned provider for Tottenham loanee Lennon to restore Everton's lead with 13 minutes remaining, while Adel Taarabt's late effort hit the bar as the hosts fell to their fifth consecutive Premier League defeat.