Just as he had in the 2-2 FA Cup draw at Upton Park in January, van Persie found the net in front of the Sir Trevor Brooking Stand to rescue United from being penalised for a sluggish display.
West Ham had looked set to earn a hard-fought win through a vicious strike from Mohamed Diame, who restored the hosts' lead early in the second half after Antonio Valencia cancelled out Ricardo Vaz Te's opener.
With second-place Manchester City having beaten Wigan Athletic, United now require six points from their final five games to secure a 20th English league title.
Their lead is now 13 points, but while a late collapse appears unthinkable, manager Alex Ferguson will be concerned by the apathy that has crept into his team's play.
"We had to stand up to a lot there but they kept going, our players - down twice, come back. Played like champions, I thought," Ferguson told Sky Sports.
"Magnificent, in terms of determination and courage to play, so I was pleased with the result."
West Ham, meanwhile, climb one place to 11th -- one point short of the 40-point mark -- and their top-flight status seems all but secure.
However, manager Sam Allardyce was aggrieved that van Persie's goal was given despite an apparent offside.
"We had a fabulous win taken away from us by an assistant referee with Robin van Persie's equaliser," he said.
"We would have been satisfied with a draw before the start but when you see a victory against one of the best teams in Europe taken away from you, it's hard to take."
Allardyce is eager to tie on-loan striker Andy Carroll to a permanent contract and the Liverpool man demonstrated his worth with a brilliantly uncompromising display.
The West Ham number eight was the first player to threaten at either end, showing great footwork to shield the ball from a posse of defenders before dispatching a low shot that grazed the right-hand post.
James Collins glanced a Gary O'Neil corner over the bar, before the hosts' positive start received its reward in the 17th minute.
Carroll was the key link in the chain at the end of a swift counter-attack, nodding the ball down for Vaz Te to score with a diving header after Matt Jarvis surged past Rio Ferdinand on the left.
United's frustration told with a hopeful shot off target from Wayne Rooney, restored to a striker's role after his stint in midfield at Stoke City on Sunday, but in the 31st minute they levelled.
It was the first piece of quality in attack the visitors showed, but it was devastating with Van Persie slipping a pass inside to Shinji Kagawa, whose shimmy took him past a defender and allowed him to centre for Valencia to tap home.
In reply, Diame hit the side netting for the hosts, while home skipper Kevin Nolan had a penalty appeal turned down after tangling with Nemanja Vidic just inside the United box.
Booked following a tussle with United goalkeeper David de Gea early in the second half, Carroll came close to exacting swift revenge with a dipping half-volley that narrowly missed the Spaniard's right-hand post.
If United thought they had survived the West Ham storm, they were wrong, as Diame put the hosts back in front with a fine goal 10 minutes after the interval.
Collecting a pass from Guy Demel near the United byline on the West Ham right, he span away from Rooney and set himself before bending a sweet left-foot shot into the bottom-left corner from outside the box.
United's push for an equaliser drew the best from the hosts, with O'Neil hacking a shot from Rooney off the line and goalkeeper Jussi Jaaskelainen producing a superb one-handed save to deny Van Persie.
West Ham's luck was to desert them in the 77th minute, however, as Van Persie slammed home the equaliser after Kagawa's deflected shot struck both posts.
Jaaskelainen then saved from United substitute Javier Hernandez, but defeat would have been cruel on the home side.
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