Hosts held after failing to create enough clear-cut opportunities, but can take solace in the fact that the American's goals don't look like drying up any time soon
The hosts took the lead as Dempsey turned and fired the ball in with just over 20 minutes to go, but will be disappointed not to have created more opportunities before they were pegged back by Tchoyi's late equalizer.
In the opening stages, the Cottagers seemed to be lacking a presence up front with both Clint Dempsey and Bryan Ruiz dropping in deep to get on the ball, but they had the ball in the net 10 minutes in - only for it to be chalked off for offside after Danny Murphy's through ball found the American in behind the West Brom defense.
A minute later came a real chance for the visitors. Odemwingie was played through and managed to stay onside despite Brede Hangeland's poor effort at playing him off, but the Nigerian spurned the opportunity, sending it high and wide.
Marc-Antoine Fortune then wasted another good chance for the visitors. Youssouf Mulumbu stayed strong on the ball and after some link up play with Simon Cox, Odemwingie was in down the right. He found Fortune, despite a slip, but the striker’s placed effort found the higher reaches of the Hammersmith End.
Steve Sidwell then got free in the area after a nice exchange of passes with Ruiz, but his cross/shot was overhit before Dempsey had a strike comfortably stopped by Foster in the lead-up to halftime.
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It was a relatively quiet opening to the second half in terms of chances, with neither side offering any real threat in front of goal.
However, in the space of a minute there were good chances for either side. Odemwingie got the better of Hangeland in the channel and raced across the byline, but his cut-back to Fortune was slightly behind the striker, who took a touch before driving the ball low as Stockdale made a good save.
Fulham then broke at the other end, and Ruiz drifted past a couple of defenders before his poked effort landed at the feet of Foster.
The game seemed to be drifting towards a draw until Fulham finally took the lead with just over 20 minutes to go.
Dorrans sliced a clearance straight into the air, and Sidwell nodded the ball down to Ruiz, who cleverly disguised a pass to Dempsey, and on the turn the American crashed the ball into the bottom corner.
The game was relatively quiet for the next 10 minutes, but substitute Somen Tchoyi had other ideas as he coolly dispatched the ball past Stockdale and into the far corner after Morrison's flick on with just under 10 minutes to go, a goal that secured a point for the Baggies.