Leeds started well but struggled in the second half, having fallen behind to a Luke Chadwick goal after half-time.
A Matt Etherington cross found Marlon Harewood in the area and the striker's blocked header fell into the path of Chadwick whose shot beat Neil Sullivan.
Leeds kept battling and were rewarded late on when Steve Lomas brought down David Healy in the area and he stepped up to score from the spot.
Leeds boss Kevin Blackwell:
"West Ham aren't happy with the penalty but I'm just pleased to get a very good point against a very good side.
"If the video shows that David has dived I will have a word with him.
"My lads deserve great credit for battling away and getting a great point."
West Ham: Bywater, Ferdinand, Repka, Darren Powell, Chris Powell, Chadwick (Reo-Coker 67), Lomas, Fletcher, Etherington, Rebrov (Sheringham 45), Harewood. Subs Not Used: Burch, Mullins, Zamora.
Booked: Darren Powell
Goals: Chadwick 50
Leeds: Sullivan, Kelly, Butler, Kilgallon, Pugh, Richardson, Gregan, Wright (Walton 90), Oster (McMaster 86), Healy, Deane (Joachim 80). Subs Not Used: Carson, Spring.
Goals: Healy 90 pen
Ref: M Pike (Cumbria)