United were twice forced to come from behind for a share of the spoils with goals from Antonio Valencia and van Persie cancelling out efforts from Ricardo Vaz Te and Mohamed Diame.
The draw leaves United 13 point clear at the top of the table, while the point all but secures West Ham' Premier League safety.
West Ham started on the front foot and in-form striker Andy Carroll went close to scoring after just five minutes when he fired in a shot from the edge of the box which flew just wide of the far post.
The home continued to push forward and they made their early pressure count on 16 minutes when Ricardo Vaz Te found the net from close-range with his first goal since October. Matt Jarvis beat Rio Ferdinand down the right before hanging up a cross to the far post for Carroll to head back across goal to allow Vaz Te to nod the ball home from four yards out.
After a slow start United finally sprung into life just past the half hour mark as Antonio Valencia drew the visitors level with his first Premier League goal of the season. Shinji Kagawa was the architect of the goal as he played a neat one-two with Robin van Persie to get into the West Ham box before crossing for Valencia to fire home the simplest of finishes inside the six-yard box.
The first half ended in controversial fashion when Carroll caught De Gea with robust aerial challenge from a West Ham corner much to the annoyance of Sir Alex Ferguson on the sidelines.
United really should have taken the lead seconds after the restart when Wayne Rooney picked out van Persie inside the box with a perfect pass and he headed the ball down into the path of Jones only for the youngster to get his shot all wrong in front of goal.
The impressive Carroll was inches away from restoring West Ham's lead on 52 minutes with an ambitious left-footed half volley from fully 30 yards out which flew just wide of a worried De Gea's goal.
Three minutes later West Ham hit the front again with a stunning strike from Diame. Guy Demel found Diame on the edge of the box and he brilliantly turned Rooney before firing an unstoppable left-footed shot into the bottom far corner to send the home fans into raptures.
United went close to equalising for a second time on 63 minutes when van Persie picked out Rooney from a well-worked corner and his shot was kicked off the line by Gary O'Neil.
The league leaders drew level on 13 minutes from time when van Persie was on hand to fire high into then net after Kagawa's superb effort came off both posts.
United threw everything at West Ham in the closing stages, but the closest they came to a winner was when Jussi Jaaskelainen produced a smart save from substitute Javier Hernandez's header.