Substitute Berbatov tapped in from close range after 88 minutes to send Sir Alex Ferguson's team five points clear at the top and earn sighs of relief from his side, who had been reduced to 10 men after the dismissal of Jonny Evans.
Arsenal staged a fightback from two goals down at the Hawthorns but could not find a late winner of their own.
Watched from the Old Trafford stands by Ferguson, who was serving the first of a five-match touchline ban for improper conduct, United went a man down after Evans, the Northern Ireland defender, was shown a red card in the 76th minute for a bad tackle on Bolton's American midfielder Stuart Holden.
"The players deserve all the credit they get," Ferguson told Sky Sports.
"You've got to remember, the last five games we've had two European ties against Marseille, (and games against) Chelsea, Liverpool and Arsenal - it's a hell of a programme. They've come through it."
Arsenal's confidence had been crushed recently after losing the League Cup Final and tumbling out of the Champions League and FA Cup, but they produced a spirited second-half performance against West Brom.
Arsene Wenger's side got off to the worst possible start when they left Reid unmarked and the West Brom defender jumped to head in Chris Brunt's corner in the third minute.
The visitors gave themselves hope after 70 minutes when Arshavin smashed the ball into the top corner from just outside the area, and the comeback was completed eight minutes later when Van Persie's shot was deflected in by Abdoulaye Meite.
"Of course (we're) disappointed that we dropped two points but it was psychological for the rest of the season - it was important for us to show character and not lose the game," Wenger said.
