There are still seven points separating the Manchester clubs after United and City registered victories on an incident-packed Super Sunday.
Manchester United held off a late Liverpool rally to beat their old rivals 2-1 at Old Trafford and tighten their grip on top spot in the Premier League.
But substitute Daniel Sturridge’s first Premier League goal for Liverpool brought the visitors back into the game and there were one or two nervy moments before the Red Devils confirmed the three points.
United took the lead with the opening chance of the game on 19 minutes when Van Persie swept home first time from Patrice Evra’s low cross following a patient build-up by the leaders.
The Red Devils should have extended their lead just before the break, but Van Persie’s flick from Rafael’s cross was cleared off the line by Martin Skrtel and Pepe Reina was hurt in a collision with Shinji Kagawa in the scramble for the loose ball.
Both teams made half-time changes as Antonio Valencia replaced Young and Sturridge came on for Lucas, who had been booked just before the interval.
United struck again on 53 minutes when Skrtel was booked for hauling back Welbeck and Van Persie’s delivery was met by Patrice Evra, whose header was inadvertently deflected in by Vidic.
Liverpool were quick to respond and pulled a goal back within four minutes when Sturridge was sharpest to the loose ball after David de Gea could only parry Steven Gerrard’s low drive from outside the box.
Kagawa forced a flying save out of Reina with a deft curler before Glen Johnson, Sturridge and another substitute Fabio Borini all failed to find the target as the Reds pushed for an equaliser.
Manchester City beat Arsenal 2-0 in a game that saw both sides reduced to 10 men alongside a whole raft of yellow cards.
Laurent Koscielny was sent off inside the first 10 minutes for hauling down Edin Dzeko, who missed the subsequent penalty.
James Milner lashed home a 21st-minute opener after being well picked out by Carlos Tevez, before Dzeko added a second from close range when the Argentine striker’s shot was parried by Wojciech Szczesny.
Vincent Kompany was given a straight red for a two-footed challenge on Jack Wilshere 15 minutes from time, but City held on to take all three points and keep pace with their local rivals at the top of the table.