Trailing Rafa Benitez's side by two points before kick-off, the champions looked like they had missed an excellent opportunity to hit the summit against a resilient Bolton at the Reebok.
But the Bulgaria striker stooped to head home Carlos Tevez's perfect cross in the final minute to move Sir Alex Ferguson's team a point clear of their closest rivals.
The victory also saw United equal Chelsea's top-flight record of ten consecutive clean sheets.
After three successive Premier League defeats, Bolton were hoping for a repeat of last season's success at the Reebok when Gary Megson's side triumphed 1-0 - their first home success over their neighbours in nearly 30 years.
But the omens were not good for Wanderers, who have lost seven out of their last eight encounters with the champions and had not scored a goal against anyone since defeating Portsmouth on December 20.
United, without the injured Wayne Rooney after the striker pulled his hamstring in the midweek victory against Wigan, had the opportunity to pile the pressure on Liverpool ahead of their game with Everton on Monday night.
But despite dominating the early exchanges, it was Bolton who nearly broke the deadlock when Fabrice Muamba's 25-yard piledriver forced a finger-tip save from Edwin Van der Sar on 28 minutes.
Kevin Davies then saw his ambitious volley fly wide as Wanderers' confidence visibly grew.
United continued to struggle to create clear-cut chances but Cristiano Ronaldo, the newly-crowned FIFA World Footballer of the Year, finally forced Jussi Jaakelainen into action with a downward header from Darren Fletcher's cross.
The Wanderers goalkeeper then made an even better save from Ronaldo three minutes before half-time when he dived low to his left to turn aside the Portuguese star's free-kick.
Davies went even closer when he headed Jloyd Samuel's cross inches after the break over, before Jaaskelainen again denied Ronaldo when he kept out the winger's thunderous free-kick.
Ferguson threw on the experienced Paul Scholes and Ryan Giggs as United searched for a goal, but apart from another Ronaldo free-kick well saved by Jaaskelainen, they could find no way through until Berbatov's vital late contribution.