Captain Jed Wallace slotted home the opening goal on 14 minutes before Lewie Coyle scored only the third goal of his career to equalise four minutes before half-time for the visitors.
Matt Phillips grabbed his third goal of the season midway through the second half to put the hosts back in-front before Semi Ajayi secured the points with just under 20 minutes remaining.
The hosts produced a fast start with Wallace and Grady Diangana both having goal-bound attempts well blocked in the opening three minutes.
Hull though, backed by 1,780 travelling supporters, grew into the contest and Liam Delap flashed a ball across the face of goal, which nobody in black and amber anticipated, before Scott Twine appealed for a penalty after he went down under a challenge from Darnell Furlong.
West Brom took the lead through Wallace when Hull’s Jean Michael Seri gifted the ball to the forward and he calmly rolled it past Ryan Allsop for the game’s opening goal.
Hull began to dominate possession but found their opponents’ defence hard to break down.
Twine, who is yet to score for the club, struck a free kick from the edge of the penalty area straight into the West Brom wall after Kyle Bartley had fouled Delap.
However, Twine was to turn provider when his cross to the back post was met by the incoming Coyle and the Hull captain struck a volley that bounced into the far corner of the goal to bring the game level going into half-time.
Delap appealed for a penalty early in the second half after going down under the close attention of Conor Townsend.
Coyle though was again the man of the moment, this time in his defensive duties, when he put in a well-timed challenge to deny Phillips when the forward was about to pull the trigger.
There was another injury concern for Baggies manager Carlos Corberan when Bartley was forced off with a suspected shoulder injury and had to be replaced by fellow centre-back Ajayi.
The Baggies restored their advantage on 65 minutes when Diangana was released down the right wing, cut inside Jacob Greaves and showed composure to play the ball across to an unmarked Phillips who slotted the ball beyond Allsop.
Substitute Ajayi sealed the three points on 71 minutes when his shot deflected into the goal off Greaves, once again created by the good work of Diangana before the winger departed to a standing ovation.