Alan Pardew's long-awaited first win in charge looked to be on its way when Brian Deane gave Hammers an early second half lead but the Dons struck back through Jodi McAnuff to earn a point.
That was despite an attacking Hammers line-up that saw new signing Marlon Harewood make his debut alongside Deane and David Connolly in a 4-3-3 formation.
The former Nottingham Forest striker replaced Don Hutchison, as Pardew went all-out for a victory that would have taken his side back into the top seven, but Hammers never looked convincing enough to take all three points.
Connolly, Deane and Harewood all went close in the first half without causing too much trouble for Dons keeper and former Upton Park youngster Steven Banks, while the hosts' only effort of any note was an Adam Nowland shot that flew just wide.
The visitors came out for the second half in more determined mood and their approach paid off just six minutes in, when Horlock's square pass found Deane, who curled a low shot from the edge of the penalty past the diving Banks.
That should have bee the cue for Hammers to go on and win comfortably, but the relegation strugglers had other ideas and were level just 11 minutes later.
Patrick Agyemang's low cross from the right wasn't cut out by the Hammers defence and McAnuff was on hand to side-foot the ball home from six yards out.
Hammers fought back in search of a second and Harewood went close with an angled eight-yarder that Banks beat out, before Carrick saw a dipping 25-yard volley just clear the crossbar.
Hutchison came on for the tiring Deane, but Pardew's men couldn't find the breakthrough and it was left to David James to ensure that the night didn't turn even worse for his team-mates.
Having hardly had a shot to save all night, the England keeper sprung into action in the final 10 minutes with a superb double save, first blocking McAnuff's fierce 18-yarder and then blocking Agyemang's follow-up.
The result means that Pardew has now drawn five and lost one of his six league games in charge and the pressure will be on when third-placed Wigan Athletic visit Upton Park on Saturday.