Albion had to settle for a 1-1 draw at Swansea City in the Sky Bet Championship on Saturday.
The Baggies, less than 72 hours after beating Preston North End, almost claimed a victory following substitute Tom Fellows’ goal - but Joe Allen’s late leveller ensure the spoils were shared.
Next up, they break from league action and visit AFC Bournemouth in the FA Cup Third Round.
Albion made two changes as Mason Holgate and Jed Wallace came into the XI for the fifth game of a brutal two-week spell.
Swansea created the opening few chances in South Wales, only to see Liam Cullen and Goncalo Franco both guide efforts over. Josh Key also had a header cleared off the line.
However, from the 20-minute mark onwards, it was mainly the away side who knocked on the door. Molumby twice threatened, having one deflected wide and another past the post wide, while Lawrence Vigouroux excellently saved Karlan Grant’s low drive among a particularly chance-ridden spell.
Mikey Johnston tried to nudge in on the action, yet found the Swans goalkeeper in his way too, and he arrowed another strike off-target. Down the other end, Zan Vipotnik went close via a low attempt just before the interval.
Overall, there were 18 shots between the two clubs within a somehow goalless - but certainly entertaining - first period.
Swansea and Albion exchanged opportunities again at the second-half’s restart, as Josh Tymon’s volley failed to threaten Alex Palmer and Albion watched a whole host of hits get blocked.
Finally, though, the Baggies edged ahead in the 66th minute. The outstanding Molumby won possession, ran forward and fed substitute Fellows inside the box to convert a clever near-post finish.
Frustratingly, the hosts denied the away team all three points during stoppage time, when Allen nodded home an agonising equaliser.
Albion: Palmer; Furlong, Holgate, Heggem, Styles; Wallace (Fellows 57), Molumby, Diakite (Mowatt 57), Johnston (Swift 86); Grant (Diangana 81), Maja (Cole 81)
Substitutes: Wildsmith, Bartley, Taylor, Racic.