
Michael Ballack and Florent Malouda scored second-half goals to seal the win, and only United's far superior goal difference keeps them above the London side at the top of the table.
Chelsea must now beat Bolton Wanderers on Sunday and hope that United fail to win at Wigan Athletic to win the title for the third time in four years.
"Manchester United are a great team," Chelsea manager Avram Grant said. "I think we've given them a very good fight, and now we need to continue that.
"I think this is one of the best seasons. We've shown a lot of character and also good football. Unfortunately the advantage is with United but it will not be easy."
Grant admitted that his side had started slowly against Newcastle, saying they hadn't played well.
"All the last month we have improved game to game and in the first half we were very slow, movement was not very good.
"Maybe they were a little tired. They played 120 minutes against Liverpool three days ago, but they played much better in the second half."
Grant fielded strikers Didier Drogba and Nicolas Anelka in partnership at St James's Park, but Newcastle were by far the better side in the first half.
Michael Owen flicked a good chance wide early on and then saw his shot cleared off the line by John Terry as Chelsea struggled for potency.
The second half saw a totally different Chelsea as they attacked from the off, and Terry almost put them in front when he headed Malouda's corner onto the bar.
But the pressure had to tell in the end and after Malouda won a free kick just outside the area, on the right-hand side, just before the hour mark.
Drogba's free kick found an unmarked Ballack, who flicked his header into the corner past Steve Harper in the Newcastle goal.
Owen almost got on the end of a mishit shot by Nicky Butt, but Chelsea brought on Frank Lampard for Anelka and the England midfielder's pass set Malouda in on goal and the Frenchman slipped the ball past Harper for Chelsea's second eight minutes from time.
Terry admitted that his side had needed a tough talking to from their manager after a tame first-half showing.
"We got a bit of a rollicking at half-time," he said.
"But all we can do is our job and it's what we did. I should have scored with my header really, I was a bit disappointed with (myself) but the boys got the goals so I am really happy."
While Bolton are still not mathematically safe, Wigan are safe but Terry said he was sure they would be professional when they take on United.
"They (Wigan) are on a great run at the minute," Terry said. "They came to the Bridge and put on a big performance. Wigan are safe now but hopefully, with a great manager like Steve Bruce, they're going to go for it."