United were dominant for the first hour with two goals for the Bulgarian striker, but two strikes in six minutes by Steven Gerrard dragged Liverpool level before Berbatov won it six minutes from time.
Chelsea made it five wins out of five with 21 goals and one conceded after they ripped through promoted Blackpool with first-half goals by Salomon Kalou, Florent Malouda (two) and Didier Drogba.
The champions top the standings on 15 points, four clear of United and Arsenal, who drew 1-1 at Sunderland on Saturday.
Manchester City moved up to fourth on eight points after beating Wigan Athletic 2-0 with goals by Carlos Tevez and Yaya Toure.
Tottenham Hotspur, 3-1 comeback winners over Wolverhampton Wanderers on Saturday, are fifth on eight points and last season's top-five finishers now occupy the first five slots.
In the day's big game at Old Trafford, United were in total control after Berbatov headed in a 42nd-minute corner and added a brilliant second by bringing down a cross on his thigh with his back to goal and scoring with an overhead-kick.
Liverpool, who had offered nothing in attack, then profited from rash defending which allowed Gerrard to pull one back with a penalty after 64 minutes and equalise with a free-kick six minutes later.
United had shipped late equalisers against Everton and Fulham in recent weeks but this time they conjured up a winner as Berbatov headed his seventh goal in six games this season.
"I was saying to myself it's going to be 10 but you end up 2-2; it was a travesty of a scoreline but a great result in the end," manager Sir Alex Ferguson told Sky Sports.
For the second week running a Drogba corner helped Chelsea into the lead inside two minutes, this time an unmarked Kalou tucking in at the far post.
Drogba also provided the second after 13 minutes, crossing low for Malouda, then the Ivorian striker got on the scoresheet when he swivelled on the edge of the box to bang in the third via a deflection.
Malouda cracked in his second after a Kalou pull-back four minutes before half-time.
Chelsea's fans sat back awaiting more goals but a combination of better Blackpool defence and a drop in attacking intensity led to a scoreless second period.
"It's fantastic, through the years we improve and we try to score as many as we can," Drogba said.
"We scored four in the first half and in the second we had so many chances so maybe this is something we have to think about even if the result was great."
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