Hernandez opened the scoring with just 37 seconds gone and Vidic added a second before Frank Lampard’s second-half effort gave the hosts an anxious final quarter.
But United, who will face Barcelona in the Champions League final on May 28, held on for a win that moved them six points above Chelsea with just two matches remaining.
United can wrap up the title with a point from either of their final two matches, at Blackburn next weekend or at home to Blackpool on the final day.
They currently sit level with Liverpool on a haul of 18 titles and their next victory will make them the most successful side in England.
United gave themselves the best possible start by taking the lead with just over half a minute gone thanks to a slip from Chelsea defender David Luiz.
Ryan Giggs passed to South Korea's Park Ji-Sung whose pass sought out Hernandez. The Mexican was put through on goal by Luiz’s slip before he guided a low shot past Petr Cech in the Chelsea goal.
United looked in determined mood and Wayne Rooney almost added a second with a drilled effort from 30 yards that was pushed wide by Cech.
Chelsea knew they had to win and that desperation was reflected in Didier Drogba’s attempt to beat Edwin van der Sar from 45 yards.
United were doing all the real pressing and went close again when Park’s clipped cross was just missed by Hernandez after the ball dropped over Luiz.
And Rooney threatened again when he picked the ball up from Antonio Valencia and thumped another effort just wide.
In Chelsea’s first decent attack, Drogba headed straight up in the air from Florent Malouda’s cross and after Van der Sar punched away, he got back up again to hold Salomon Kalou’s rebound.
Cech was in top form again to tip away a powerful curing shot from Park but the Czech goalkeeper could do nothing about United’s second.
From a short corner, Giggs clipped over a cross and Vidic got in front of fellow Serbian Branislav Ivanovic to head in from close range.
The visitors almost responded immediately when Malouda’s corner was flicked on by John Terry and Kalou’s close-range header was turned away by Van der Sar.
Drogba also had a free kick beaten away by Van der Sar before curling another one wide of goal.
Both managers made changes at the interval, with Carlo Ancelotti bringing on Ramires and Alex for John Obi Mikel and the seemingly injured Luiz, while Jonny Evans came on for John O’Shea.
The visitors were fortunate not to concede a penalty when Valencia’s cross appeared to strike Lampard on the hand.
Just before the hour, Ancelotti also threw on Fernando Torres to attempt to bring some life into his side.
Alex tried his luck from 30 yards, giving Van der Sar a simple save, as the visitors struggled to penetrate.
And the Dutchman was also quickly off his line to gather a deflected Ramires cross, with Drogba poised to pounce.
But in the 68th minute, Chelsea pulled one back when Ramires’ cross was flicked on by Ivanovic and prodded in by Lampard.
United could have restored their lead just over a minute later when Hernandez broke through and squared for Rooney only for the England striker to be denied by Alex’s block.
Torres also had a penalty appeal turned down in the closing stages, before Rooney’s low effort from Evans’ pass ran just past the post.
Rooney wasted another great chance to seal the game when he was put through only to be held up and moments later his shot from just outside the area was deflected over by Alex.
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