Arsenal clung on to a 2-2 draw at Southampton with 10 men after Mathieu Flamini was sent off in the 80th minute for a two-footed tackle.
After trailing through Jose Fonte's goal, Arsenal led briefly at the start of the second half when Olivier Giroud and Santi Cazorla scored but Adam Lallana quickly leveled for Southampton.
While Arsenal extended its lead to two points, Manchester City can now go top with a victory at Tottenham on Wednesday. If City slips up, Chelsea can take the lead by beating West Ham.
Liverpool's focus is Champions League qualification, and a 4-0 derby demolition of Everton - with Daniel Sturridge scoring twice - took them three points ahead of Tottenham in fourth place.
United is staying in touch with the top four, but remains six points adrift despite Van Persie taking just six minutes to score after almost two months out in a 2-0 victory over bottom-place Cardiff.
Jonjo Shelvey and Chico Flores scored as Swansea beat Fulham 2-0 for its first win in nine league games, while Jason Puncheon eased Crystal Palace's relegation fears by clinching a 1-0 victory over Hull.
The only game without goals on Tuesday was at Carrow Road, but the drama was provided by the 80th-minute scuffle that led to Norwich midfielder Bradley Johnson and Newcastle striker Loic Remy being sent off.
On the south coast, Arsenal experienced an unusually dismal first half in a bright season for Arsene Wenger's side.
Fonte rose over Nacho Monreal to meet Luke Shaw's cross to head past Wojciech Szczesny in the 21st.
Arsenal avoided conceding again, and turned the game around after the break, with Giroud deflecting Bacary Sagna's cross into the net in the 48th and Cazorla set up by Mesut Ozil for a goal four minutes later.
But Southampton became just the second side to score more than one against the Gunners in their last 22 league games when Lallana scored from Jay Rodriguez's cutback in the 54th.
And Arsenal settled for the point after Flamini saw red for a two-footed lunge on Morgan Schneiderlin.
At Anfield, Liverpool completely overwhelmed Everton after captain Steven Gerrard headed the hosts in front after 21 minutes.
Sturridge then sprung the offside trap twice in two minutes to score a brace, and Luis Suarez scored his 23rd league goal of the season at the start of the second half.
Sturridge missed out on a hat trick when he sent a penalty kick over the crossbar after Raheem Sterling was brought down by goalkeeper Tim Howard.
''It's a massive victory over rivals close to us,'' Liverpool manager Brendan Rodgers said. ''If you look at Everton they've only conceded 11 goals away from home before tonight and for us to get four and to maybe have had a few more is very pleasing.''
At Old Trafford, it was the perfect debut for record signing Juan Mata, and the perfect return for Van Persie.
''We have missed his goals,'' United manager David Moyes said.
After seven weeks out with a thigh injury, Van Persie headed United in front after six minutes, and Ashley Young struck the second after the break.