Bowen added to his growing reputation as he struck in first-half stoppage-time and converted from the penalty spot shortly after the break before substitute Fraizer Campbell underlined the home side's superiority in the last 10 minutes with the third goal.
Bowen's form has reportedly attracted the attention of Premier League clubs Tottenham and Leicester although head coach Nigel Adkins has stated the Tigers would not sell any players during January.
Wednesday clearly came to frustrate and rarely threatened the home goal, having just one effort on target in the first half and doing little more in the second period.
Without several fine saves from Keiren Westwood in the first half, the margin of defeat would have been much heavier.
The Tigers could have taken the lead in the second minute when Kamil Grosicki tried to curl the ball inside the far post with a shot from the left side of the area, but Westwood dived full stretch to his left to turn the ball around the post.
Westwood was off his line smartly to block at the feet of Chris Martin who ran on to Grosicki's pass from the edge of the area with nine minutes on the clock.
Martin then returned the compliment with a pass from halfway which Grosicki took control of before running on to shoot at Westwood as the home side continued to dominate.
Wednesday were struggling to contain Hull and their first effort on target came after 20 minutes when a shot by former Hull forward George Boyd from the edge of the area was blocked.
But for another good Westwood save Markus Henriksen would have given the home side the lead midway through the first half with a shot from the edge of the box.
Adam Reach fired well over as the visitors made a rare foray into the Hull half three minutes before the break.
Just as it looked like Wednesday would reach half-time level, Bowen opened the scoring, receiving the ball on the edge of the area before firing a low left-footed shot into the bottom-left corner of the goal.
Bowen extended his side's lead six minutes into the second half when he sent Westwood the wrong way from the penalty spot after the goalkeeper had brought down Martin as the striker ran on to a pass.
Hull continued to dominate as Jordy De Wijs headed over from a corner and Grosicki then curled the ball over the crossbar.
The home side deservedly made it 3-0 with 14 minutes to go as substitute Campbell beat Tom Lees to a bouncing ball on the edge of the box before shooting powerfully past Westwood to wrap up the victory.
Grosicki might have made it four six minutes from the end but for a fine late challenge by Michael Hector to block the winger's shot – but for Wednesday, the damage had already been done.