The 19-time league champions had Michael Carrick open the scoring inside five minutes before Robin van Persie broke a 10-game scoring drought from the penalty spot in the 66th minute to lead United to their 26th win of the campaign which saw them bounce back from Monday's derby loss to Manchester City.
The victory allowed United to again go 15 points clear of second-placed City who are into the FA Cup final after beating Chelsea 2-1 in the semi-final at Wembley, also on Sunday, whilst the Potters dropped to 16th.
Arsenal are now third after producing a late fightback to beat Norwich City 3-1 thanks to goals from Mikel Arteta, (penalty), Olivier Giroud and Lukas Podolski following Michael Turner's 56th minute opener.
Arteta equalised in the 85th minute after Kei Kamara was adjudged to have pulled the shirt of Giroud in the area, which was spotted by assistant on the far side, before Giroud prodded home Alex Oxlade-Chamberlain's low cross. The win was complete when Podolski fired home from 18 yards in injury-time to push Arsene Wenger's men into a Champions League position.
Just one point behind them are Chelsea, who have a game in hand, and North London rivals Tottenham who are still due to take on the Blues.
Elsewhere, Aston Villa missed a golden opportunity to go clear of the drop zone by conceding an own-goal to allow 10th-placed Fulham to force a 1-1 draw, Everton beat QPR 2-0 to heap more misery on the Londoners, bottom-placed Reading held Liverpool to a 0-0 draw at home as Andy Carroll levelled for West Ham United in their 1-1 draw at Southampton.
2012/13 Barclays Premier League season scores