The hosts went into the lead midway through the second half, as Clint Dempsey opened the scoring on 69 minutes, but a Somen Tchoyi equaliser eight minutes from the end ensured spoils were shared.
Home boss Martin Jol was slightly disappointed to concede in the last ten minutes, but all in all was happy with a point.
“To concede a goal in the last eight minutes was disappointing but I was happy,” the Dutch manager told Sky Sports.
“You always have to make a difference against teams like this, they played very well, were well organised and you need patience and still play in a good tempo.
“And I think in the second half we did that. In the first half we didn’t.
“So the extra quality came from Bryan Ruiz and of Clint Dempsey, you know that he’s a goal scorer,” Jol concluded.
West Brom host Swansea next on Saturday, whilst the Cottagers travel to take on league leaders Manchester City at the Etihad Stadium.
By Gareth McKnight