The Hammers led twice and looked to be heading for a third straight win when Patrick Kisnorbo's own-goal made it 2-1 in the second half.
But as the clock ticked down Leeds, who earlier missed a penalty through Max Gradel, snatched an equaliser through 22-year-old midfielder Clayton.
Sam Allardyce's side, beaten by a last-gasp goal by Cardiff in their last home game, had since recorded two victories on the road by grabbing early leads and they repeated the trick in the sixth minute at Upton Park.
Leeds goalkeeper Andy Lonergan had already tipped over headers from Carlton Cole and James Tomkins, but he was beaten when Matt Taylor swung in a second corner.
Cole got in front of his marker and guided a volley past Lonergan with the outside of his right boot for his second goal in as many games.
Leeds, playing to a backdrop of 'we are the morons' from the away end - a reference to chairman Ken Bates' pet name for their disgruntled fans - attempted to hit straight back and Green turned an angled drive from Gradel over the top.
Moments later, a deep cross from the right found Robert Snodgrass on the left corner of the West Ham penalty area and his volley crashed back off the near post.
The visitors were presented with a route back into the game in the 28th minute when Taylor controlled the ball with his arm in the box and referee Michael Oliver pointed to the spot.
But Gradel, the subject of a failed bid from West Ham earlier in the summer, did not impress his suitors as his penalty rolled meekly past Green's right-hand post.
Leeds were cranking up the pressure, though, and it finally told in the 59th minute when Andy Keogh and Robert Snodgrass combined well for the latter to cross low into the path of McCormack, who swept the ball past Green.
But all their good work was undone three minutes later when substitute Julien Faubert crossed from the right and Kisnorbo, in attempting to clear the ball, succeeded only in smashing it past Lonergan and into his own net.
West Ham should have added to their lead but Lonergan kept out a point-blank effort from Winston Reid and Scott Parker - being watched by England boss Fabio Capello - shot against a post.
And they were made to pay on the stroke of full-time when Jonathan Howson's shot came back off the crossbar and Clayton buried the rebound to nick a point.