Kamil Zayette fired them in front in the 47th minute, Geovanni started and finished the move that led to his fourth goal of the season before Marlon King set the seal on their success.
While Hull were potent in attack, Albion lacked a real cutting edge although they were frustrated by the woodwork and goalkeeper Boaz Myhill when they did threaten.
Albion, who have now conceded seven goals in their last two games, wasted three golden chances to break the deadlock in the space of five frantic seconds in the ninth minute and will look back on that as a match-turning moment. Borja Valero saw his 20-yard drive palmed out by goalkeeper Myhill. The loose ball looped up into the air and was met by Albion centre-half Jonas Olsson whose header cannoned off the bar. Roman Bednar then latched on to the rebound but the former Hearts striker was only able to shoot into the side-netting.
Having managed to survive that quick-fire onslaught, Hull proceeded to trouble Albion on the break and with better finishing would have taken control of the game before half-time.
King flashed a shot just wide and Geovanni was denied by goalkeeper Scott Carson before Ian Ashbee whistled a close-range shot inches the wrong side of the post.
Zayette then squandered a golden chance to put Hull in the driving seat from Dean Marney's 30th-minute corner, failing to get his close-range header on target.
Albion should really have taken advantage of that let-off seven minutes later when a probing ball by Valero picked out Ishmael Miller who surged into the area only to see Myhill tip his right-footed shot around the post.
It was a vital save by Myhill as Hull came storming out of the blocks at the start of the second half and ended the game as a contest with a devastating spell.
Geovanni saw his deflected 47th-minute shot tipped around the post by Carson and from the resulting corner by Dean Marney, Zayette fired home an unstoppable right-foot volley from eight yards.
While Ryan Donk briefly threatened to grab an equaliser when his header was cleared off the line by Sam Ricketts, the confidence noticeably drained away from Albion after Zayette's strike and Geovanni took full advantage of that to double Hull's lead in the 62nd minute. He flicked the ball into the path of King and then ran forward to meet his lay-off with a low diving header.
The impressive King deserved a goal of his own after an electric display and he was rewarded four minutes later when he latched on to Gianni Zuiverloon's misplaced header before placing his low shot past Carson.