Cole, 31, returned to his boyhood club on a free transfer from Liverpool this week, and rolled back the years as he set up a double for defender James Collins with superb crosses from the left flank in each half to turn the tie around after Tom Cleverley had fired United into the lead on 23 minutes.
However, as the clocked ticked into stoppage time, Dutchman Van Persie, who had started on the bench, ghosted into the right side of the penalty area, before drilling a low shot into the bottom corner to force a replay.
United thought they had gone ahead on 16 minutes when Danny Welbeck swept home a low cross from Javier Hernandez, but the offside flag was up against the Mexican.
It was, however, 1-0 to United on 23 minutes. More slick play down the right from Rafael released Hernandez. His low centre went all the way across into the path of the advancing Cleverley, who swept a brilliant first-time effort back past the keeper into the bottom corner.
On 27 minutes as the home side levelled.
The ball was pushed out to Joe Cole on the left, and his floated centre was met with a powerful header by centre-back Collins, which left United keeper David De Gea rooted to the spot as the ball flew into the net.
West Ham turned the tie around on the hour mark. Joe Cole was again the provider, as he floated over a perfectly-weighted ball from the left which Collins again met with a powerful header into the far corner.
With 23 minutes left, Sir Alex Ferguson had seen enough, making a double change as Van Persie and Antonio Valencia replaced Hernandez and Paul Scholes.
And Van Persie broke into the right side of the penalty area on to a superb cross-field pass from fellow substitute Ryan Giggs, held off James Tomkins and expertly drilled the ball into the far corner to force a replay back at Old Trafford.
- Sports & Recreation
- James Collins
- Javier Hernandez
- Tom Cleverley