A cagey affair was blown wide open by Albion's Josh Maja, whose creative flick inside the area saw him claim his eighth goal of the season just before the break.
Chong's surging run and finish may have bought boss Rob Edwards more time after a difficult return to the second tier had seen the Hatters start the evening in the relegation zone.
Luton dominated the ball in the early stages as their intensity and physicality prevented Albion from getting a foothold in the game on an atmospheric night at Kenilworth Road.
Despite enjoying the bulk of the possession, the Hatters initially struggled to find the final pass to unlock the back line, but a neat ball through to Carlton Morris saw the striker test keeper Alex Palmer before Victor Moses scuffed the first-time rebound wide of the post.
Chong looked the Hatters' brightest spark and the former Manchester United academy graduate consistently commanded play.
Edwards afterwards talked up Chong, who helped Luton grab a vital point after successive defeats to Sunderland and Coventry.
"He was really good, we know he's got it, he won a penalty last week and scored tonight," Edwards said.
"He's got loads of quality, we want him to believe and be free in those areas."
West Brom boss Carlos Corberan admitted his team didn't deserve to take the lead.
"We didn't deserve to be winning the first half because Luton was playing better than us. The only chance we had, we scored," said Corceran.
"We didn't impose our identity to perform. In general we did not do well enough."
A fifth successive draw means WBA, who won five of their opening six matches, are seven points behind leaders Sunderland having played a game more.
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