Baros scored the second from close range straight after the start of the second half, then Owen added another with a right-footed shot - his 100th Premiership goal.
It was not long before Owen scored his third and Liverpool's fourth after combining well again with Baros.
Gary Megson's side, already relegated to Division One next season, struggled to match Liverpool's quality and it was not long before the lead was extended once again.
Owen scored his fourth on 67 minutes, and Baros added a late goal to make the final score an impressive 6-0.
With Chelsea only drawing 1-1 at home to Fulham Liverpool must now believe that they are on their way to that fourth place.
West Brom: Hoult, Balis, Gregan, Wallwork, Clement, Johnson, McInnes, Koumas, Udeze, Dichio, Roberts. Subs: Murphy, Dobie, Jordao, James Chambers, Lyttle.
Liverpool: Dudek, Carragher, Hyypia, Traore, Riise, Diouf, Murphy, Hamann, Gerrard, Owen, Baros. Subs: Smicer, Heskey, Arphexad, Diao, Cheyrou.
Referee: D Gallagher (Oxfordshire)