Burnley started strongly in the second half, Robbie Blake forcing a good low diving save from Cudicini, and later hitting a post with a rebound from an acuteangle after the goalkeeper fumbled a free-kick.
Kevin Campbell threatened for the Baggies, stinging Jamie Ashdown's fingers with a shot from an acuteangle, while Aliou Cisse drove wide for Pompey from 25 yards.