Seeking to avoid a club record fourth successive home league loss at the start of a season, the Tigers stopped the rot after being sent on their way by a timely third-minute strike from Bowen, his first in the league on home soil in 2018 - and third in successive games against Ipswich.
Irvine sealed it after being sent clear late on and he coolly stroked home past Dean Gerken, with the visitors' winless streak in East Yorkshire extending to eight matches.
For Hull, it was a welcome win bonus after six successive home reverses in all competitions, with the Tigers also recording a first clean sheet in front of their own supporters since April 7.
Hull started with intent and fine play by Fraizer Campbell, who posed problems throughout the first half for Town's hesitant defence, soon sent Bowen clear down the right and he dinked the ball past past Dean Gerken and despite the attempts of Matt Pennington, the Ipswich loanee could not prevent the ball from crossing the line.
Showing fluency coming forward and utilising the flanks, Hull posed problems for the visiting rearguard, with a last-ditch block denying Bowen and Evandro and Campbell heading chances over.
Ipswich's best chance in arrived on 15 minutes when Hull switched off following a Jordan Graham corner, with Cole Skuse heading the ball back across goal, only for Jon Nolan to glance wide with the goal at his mercy.
Nolan also blazed over when well placed just before the interval after an error from Stephen Kingsley in a half which saw home midfielder Daniel Batty taken off with injury just before the interval - to be replaced by Kevin Stewart.
After a subdued start to the second period, Hull started to find their feet with Campbell glancing wide following an excellent centre from Reece Burke, operating at right-back, before Gerken spilled a low angled shot from the Tigers' forward before Jonas Knudsen cleared the loose ball.
At the other end, in a more even half, Ipswich attempted to prize open the door with a chance manufactured for Jordan Graham, whose low curler was held by David Marshall.
Hull spurned a chance to kill the game 20 minutes from time when the ball broke inside the box for Evandro, who lofted a close-range effort over Gerken, with Matt Pennington, stationed just in front of his own goalline, fortunately on hand to clear.
Gerken then did well to block Bowen's effort with his legs after the home winger cut inside adeptly and more smart work saw him save the day and deny the same player again following a defence-splitting pass from substitute Jackson Irvine.
It was Irvine who sealed it late on as Hull savoured a much-needed home success.
Nigel Adkins was delighted with his team’s performance and a victory which lifts them to 17th.
“Three points, a clean sheet, first home win of the season, dogged performance - well done to the players and well done to the supporters,” said Adkins.
“The last home game we played some really good football. Today was different, we started off really well getting the goal through Jarrod Bowen and then for me, it was stop-start in the second half.
“We get into half-time 1-0 up, the goalkeeper has made two really good saves from Jarrod Bowen, and it was that dogged performance from us. Towards the end, the second goal we’ve gone and scored was really good play, Jackson Irvine has showed fantastic desire and tenacity to outmuscle the defender and go for it.”