West Brom went close through Do-Heon Kim and Ishmael Miller, who both forced Manuel Almunia into action, while Johan Djourou made a clearanceoff the line.
Galway could have been even further ahead at that stage as Barry Monaghan had made a desperate clearanceoff his goal line after a Nicky Joyce shot evaded Michael Boyle.
Whittaker, a scorer the last time these two sides met in 2008, was unsuccessful with a delicate lob when the ball broke to him in the box off a headed clearance.