Even so Wanderers never stopped going forward and for long periods it looked as if Albion were the disadvantaged side.
Youri Djorkaeff missed out on a chance to equalise early on but Albion will rue the opportunity that passed them by when Roberts fired straight at the keeper in the 60th minute when he could have sealed the points.
All Wanderers' problems stemmed from a catastrophic three minutes in the first half.
First they had Ivan Campo yellow carded for a dreadful foul on Roberts and when Neil Clement's shot from the resulting free-kick fell at the feet of Dobie he turned to fire a right-foot shot past Jussi Jaaskelainen.
Three minutes later that problem was compounded when French defender N'Gotty was sent off for retaliating after being fouled by Roberts.
Campo was lucky to escape a second yellow card after a dubious looking tackle on Roberts but for the rest of the half Albion were content to soak up any pressure the home side could offer and most of that came from the trickery of Jay-Jay Okocha.
He turned on his skills to dance past defenders but for all that the only serious danger to the visitors goal was a shot that flashed narrowly past a post.
Wanderers kicked off the second half with Michael Ricketts replacing Dean Holdsworth and he created the chance of the game in the 61st minute with a superb cross for Djorkaeff to run clear into the six-yard box but the Frenchman's point-blank range shot was saved by Russell Hoult.
At the other end Roberts should have made sure for Albion but when he went clear on Jaaskelainen the keeper was able to make the save.
Albion continued to soak up Wanderers' waves of attacks but were caught out in the 88th minute when Danish midfielder Per Frandsen headed in Simon Charlton's cross at the far post