A Jonny Evans own goal after good work by Daniel Sturridge gave The Blues a 1-0 lead at half time, before a stunning volley from Juan Mata doubled their lead in the first minute of the second period.
Three points looked all by guaranteed when a David Luiz header took a deflection off Rio Ferdinand and beat David De Gea in the United goal, putting Chelsea three goals to the good.
However Sir Alex Ferguson’s men fought back courageously, with two Wayne Rooney penalties getting them within touching distance, and substitute Javier Hernandez heading home the equaliser with six minutes remaining.
Villa Boas was clearly frustrated by dropping two points, and questioned Howard Webb’s decision-making process in the second half.
“Of course, it’s not easy to take. A game where we were very positive and had the initiative for most of it,” the Portuguese coach told Sky Sports.
“It’s a massive recovery for United. It’ll feel like a win for them, of course. We had it in our hands and let it slip.
“There were some strange decisions today though. At Old Trafford we lost two goals that were offside and I see Sir Alex speaking about the linesman just after they recall him.
“These things just keep happening. The first one is a penalty and I agree with it. The second is very, very unlucky.
“I’m not sure if Howard is trying to compensate for something,” he concluded.
Meanwhile, despite staring defeat in the face, Ferguson feels that his side should have taken all three points and were the better team throughout.
“We had two penalties in the second half which were justified. I think we could have had four penalties.
“It’s two points dropped to be honest with you. We played ever so well apart from the period directly after half-time when we lost two goals. I thought we were by far the better team,” he defied.
The result means United are two points adrift of cross-town rivals Manchester City at the Premier League summit, whilst Chelsea move a point closer to Tottenham in third for the time being.
By Gareth McKnight