It looked as though it would be a happy 51st birthday for Mark Hughes as Victor Moses bundled home from close range in the first half and Mame Biram Diouf doubled the advantage from Jonathan Walters’ cross shortly after the break.
But West Ham halved the deficit on the hour mark when Downing whipped in an excellent ball for Enner Valencia to nod in. The visitors had barely threatened up until that point but they levelled in the 72nd minute when Downing drilled in a shot that Asmir Begovic could not keep out.
The draw sees West Ham drop to fifth spot in the Premier League while Stoke slip down to 12th.
And the Hammers’ comeback is even more impressive considering they were without injured top scorer Diafra Sakho and struggled in the early stages against a lively Stoke side.
The hosts carved out the first opening in the ninth minute when Geoff Cameron crossed from the right for Bojan but his effort was well blocked by James Collins. The right-hand side would prove to be a rich outlet for Stoke and they created another chance from there midway through the half when Bojan fired a wicked ball across the six-yard box that Diouf was just inches away from tapping in.
West Ham’s early frustrations were added to when Winston Reid picked up an injury and had to be replaced by James Tomkins. But they could have taken the lead after 28 minutes as Alex Song teed up Downing with a delightful backheel but the winger fired wastefully over the bar.
Minutes later the hosts edged ahead when Bojan saw a shot blocked by Collins and the ball fell to Moses, who managed to bundle it in from close range. It was no more than Stoke deserved and they almost doubled their advantage on the stroke of half-time when Diouf turned Collins but saw his shot brilliantly saved by Adrian.
Still, it didn’t take Stoke long to make it 2-0 after the break as Walters did well to win the ball on the right and crossed for Diouf to head home. At that stage there only looked to be one winner and Moses almost made sure of victory as he curled an effort narrowly wide of the post.
But the Hammers proved that they are more than up for the fight as they staged a superb comeback in the final 30 minutes. They halved the deficit on the hour mark when Downing burst free down the right and curled in an excellent cross that Valencia stooped to head home.
Stoke were aggrieved that play was not stopped in the build-up after a tough tackle by Song but they should have restored their two-goal advantage in the 70th minute when Diouf headed wide after a fine free-kick from Erik Pieters.
The miss proved costly as just a couple of minutes later Valencia did well to pull back a cross to the penalty spot where Downing lashed a shot past Begovic.
Both sides pushed hard for a winner in the closing stages but neither could carve out another real opening. Geoff Cameron had an effort palmed away by Adrian while Begovic did well to stand up and deny Valencia at the other end.