His well-taken effort, seconds from the end of the first half, was greeted by Hammers fans as if it had won them and not United the Premiership title.
Slipshod defending by United saw Bobby Zamora beat Gabriel Heinze in an all-out challenge 30 yards from goal.
The ball went to Tevez and the Argentinian easily shook off weak challenges by Michael Carrick and Wes Brown before turning his eight-yard shot beyond United goalkeeper Edwin Van der Sar and into the net.
News of the goal must have gone down like a lead balloon at Bramall Lane, where Sheffield United and Wigan were also battling for top-flight survival.
But its ramifications are sure to rumble on well into the summer as those two clubs, Charlton and Fulham continue to contest the punishment meted out to the Hammers by Tevez's controversial move.
Tevez scored the vital goal for the Hammers, but the real hero of a dramatic rain-soaked Old Trafford afternoon was goalkeeper Robert Green.
On this form, Green is sure to turn up the heat on Tottenham's Paul Robinson and United's Ben Foster for the England number one jersey.
Green produced four magnificent saves and enjoyed a near-faultless display.
At the other end, Van der Sar often looked shaky and he could be under real pressure for his place from Foster - returning from a loan spell at Watford - next season.
United manager Sir Alex Ferguson promised to field a strong team against the Hammers, but Rio Ferdinand, Nemanja Vidic, Cristiano Ronaldo, Ryan Giggs and Paul Scholes were all missing from the starting line-up, although the last four were all on the substitutes bench.
The only time Green was beaten came in a first half of few chances in the 31st minute.
Alan Smith connected perfectly with Carrick's corner 12 yards out. The shot was heading for the top-right corner of the net until Yossi Benayoun's timely intervention saw him head the ball off the line.
The rebound fell to Kieran Richardson, whose shot was blocked by Green and cleared by Benayoun.
West Ham's goal forced United to respond early in the second half and Giggs, Scholes and Ronaldo all came on as Ferguson went for broke in the 58th minute.
Ronaldo proved the catalyst to pull his side from their lethargy. In the 63rd minute Giggs' free-kick from the right was flicked on by Brown and Ronaldo's 12-yard shot was superbly blocked by Anton Ferdinand.
Twelve minutes later, Ronaldo met Giggs' corner eight yards out, only to see Green brilliantly keep out his fierce header.
Green again denied Ronaldo soon after and, deep into stoppage time, hauled himself across goal to turn over Scholes' 25-yard thunderbolt.
United claimed they should have had a penalty when John O'Shea went down in the Hammers box, following a tackle from behind by Nigel Reo-Coker.
But, at the end, United were happy to celebrate hard as they were presented with their ninth Premiership trophy under Ferguson's management and can now look forward to Saturday's FA Cup Final against Chelsea at the new Wembley.
There were ecstatic celebrations from West Ham's travelling army of fans, but you can bet on the other side of the Pennines the story of that controversial transfer is not yet over.