Taylor was on target after just 14 minutes against his former club, bending the ball into the top corner of the net after a jinking run from Lloyd Dyer.
Goalkeeper Joe Murphy also impressed between the goals for Albion, making a number of crucial saves particularly from Gerald Forschelet and Derek Niven. West Brom and Tranmere have since agreed a fee for Joe Murphy, deciding not to take the matter to a tribunal.