It had been 260 days since the 24-year-old last played for the Pilgrims after tearing an anterior cruciate ligament during a League One game at Sheffield Wednesday in early February.
Cooper was not troubled too much by a West Brom side lacking some of their main attacking threats due to injuries, although he did make one good diving save in the second half.
Argyle were much the better side in the first period but could not turn their good attacking play and chances into a goal, with Morgan Whittaker coming the closest to doing so with a shot which hit a post.
There was an improvement from West Brom after the interval but the Pilgrims defended so strongly that Cooper was not called into serious action too often.
The return of Cooper was one of six changes to Argyle's starting lineup from their last match before the international break, which was the 3-1 defeat by Swansea City at Home Park on October 7.
Also coming into the side for the Pilgrims' first match at The Hawthorns since September 2009 were on-loan Aston Villa pair Finn Azaz, and Kaine Kesler-Hayden, as well as Lewis Gibson, Mickel Miller and Adam Randell.
Conor Hazard had been Argyle's 'keeper for the first 11 matches of the Championship campaign with Cooper on the road to recovery.
However, he dropped down to the substitutes' bench against West Brom, along with Matt Butcher, Luke Cundle, Joe Edwards, Macaulay Gillesphey and Julio Pleguezuelo.
Jordan Houghton was the captain for the visitors, who welcomed back Gibson after the former Everton defender had missed the previous three matches due to a foot injury.
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