The ex-Hibernian boss officially takes over on Wednesday and will inherit a winning side.
Goals from Zoltan Gera and Diomansy Kamara, his fifth in three games, at Selhurst Park followed Albion's 5-1 win at Ipswich last Saturday.
While Mowbray will start work at the training ground with a big smile, it's a different story for Palace boss Peter Taylor who had to suffer another shambolic performance from his side.
The result could have been extremely embarrassing for Taylor, as Albion took just a portion of the chances that came their way.
Gabor Kiraly in the Palace goal didn't exactly inspire confidence as he had difficulty on several occasions in dealing with Jason Koumas' in-swinging corners.
Ben Watson saved the Hungarian goalkeeper's bacon with a goal-line clearance from Kamara's header, while Curtis Davies and Nathan Ellington also headed over with Kiraly rooted to his line.
It was left to Gera to give the Baggies their inevitable lead. Ellington found space down the right and crossed waist height into the goalmouth where Gera scooped low to power his header passed the hapless Kiraly.
That goal came in first-half injury-time and three minutes after the break Kamara neatly added a second, after Koumas laid on a perfect pass into the left channel. Kamara made ground into the area before unleashing a low shot which nestled neatly into the corner of the net.
It was not a good night for Shefki Kuqi, who does not look good value for the £2.5million Palace paid for him last month and was eventually substituted.
The Eagles got slightly better and visiting goalkeeper Pascal Zuberbuhler at last had something to do with a couple of routine saves from Dougie Freedman and James Scowcroft.
Albion looked comfortable, with Jonathan Greening and Koumas in full control of midfield.
The visitors should have added a third as they had so little trouble penetrating the Palace defence, but found Kiraly in better form in the latter stages of the game
Near the end James Scowcroft struck the post, but few fans stayed around to witness it and those that did booed the home side off the pitch.