The win saw West Brom return to the top of the Championship table 45 points, two points ahead of Leeds United.
They have now won five consecutive league games and are unbeaten in their last nine.
Ajayi who made his 20th league appearances for the Baggies this season, scored in the 25th minute to open scoring.
It is his third league goal of the season so far in the current campaign.
Mathews Pereira made it 2-0 in the 34th minute before Hal Robson-Kanu added the third goal on 44 minutes.
In the 70th minute Matthew Phillips got on the score sheet to make it 4-0 while Kyle Edwards added the fifth goal on 74 minutes to complete the rout.