Norwich netted a stoppage time winner to beat Albion 1-0 on Saturday afternoon.
Josh Sargent’s 92nd-minute goal earned the Canaries all three Sky Bet Championship points at Carrow Road.
The Baggies, who remain sixth, now have seven matches remaining - with Sunderland visiting The Hawthorns next Saturday.
The boss was able to bring Callum Styles back into his starting XI for the trip to Norfolk - the left-back recovering from a calf strain - while also recalling winger Tom Fellows.
And the Baggies started brightly under the spring sunshine, forcing Angus Gunn into two early saves. First, City’s goalkeeper spilled a powerful Karlan Grant shot just wide, and then he brilliantly clawed away Torbjorn Heggem’s goalbound header shortly after.
Down the other end, Joe Wildsmith excellently stopped Sargent when the striker looked destined to open the scoring, and Ante Crnac put the rebound wide.
In the main, though, Mowbray’s men produced the better chances ahead of half-time - going close again through another Grant curler, which was saved, and seeing Mason Holgate’s tap-in disallowed for offside.
The teams began the second 45 by exchanging opportunities, but Wildsmith held Borja Sainz’s shot and Grant smashed off-target.
It was a stop-start affair and, despite Albion spending long periods camped in the Norwich half, they didn’t often test Gunn.
Grady Diangana and Mikey Johnston were introduced for the final 12 minutes as the Baggies tried to find a breakthrough.
However, the hosts were the ones to seemingly steal all three points via Sargent’s very late finish.
And they held on in the final seconds, too, clearing multiple Albion attempts off the line.
Albion: Wildsmith, Holgate, Bartley, Heggem, Styles, Molumby (Bany 85), Swift, Mowatt, Fellows (Diangana 78), Armstrong (Lankshear 85), Grant (Johnston 78).
Substitutes: Griffiths, Frabotta, Diakite, Price, Dike.