In response, visiting Sunderland went close in the 15th minute but James McClean's low effort was parried wide by West Brom goalkeeper Ben Foster.
Sunderland manager Martin O'Neill brought on Fraizer Campbell for the start of the second half to give his side a larger attacking threat.
However, the Baggies added their third of the afternoon in the 48th minute. Morrison found Marc-Antoine Fortune, who in turn crossed for Odemwingie to shoot first time past Mignolet.
Winger Thomas almost scored a fourth for the home side in the 55th minute, but his curling effort struck the crossbar.
Sunderland also hit the woodwork late in the game as England international Campbell saw his powerful effort cannon back off the bar.
There was still time for midfielder Keith Andrews to add a fourth for the Baggies when he converted a pass from Graham Dorrans in stoppage time.
West Brom have now scored nine goals in their last two matches.