Goals from Bowen and Markus Henriksen put the Tigers two up before Pawel Wszolek pulled a goal back for Rangers.
Bowen effectively sealed the Tigers' victory with 21 minutes remaining, scoring at the second attempt after being set up by Kamil Grosicki.
Luke Freeman reduced the deficit in injury time by adding the finishing touch after Bright Osayi-Samuel's cross had been headed down by Tomer Hemed.
But Steve McClaren's side were unable to avoid only their fourth defeat in 16 Sky Bet Championship matches - a run stretching back to August.
Hull manager Nigel Adkins revealed a pre-match pep talk did the trick for Bowen, who was outstanding throughout.
Bowen, who opened the scoring after just six minutes, had netted just once in his previous nine matches.
“Jarrod hadn’t scored for a few weeks and I said to him before the game to just go and enjoy playing football,” Adkins revealed.
“Sometimes things can start to build up a little bit and you just need to go and enjoy playing football.
“You can see he had that today and he worked for the team, scored two and could have had a couple more.”
The victory lifted City out of the bottom three and was their second win in their past three away games.
“I’m really pleased for all the staff and players. We’ve come away from home and again played really good football,” Adkins said.
“We’ve got a team that are so committed to the cause. The team ethos is there and they’ve run their socks off.
“They’ve competed and without any individual the whole team have just worked their socks off again.
“We’ve been playing good football but been caught out by individual mistakes that have cost us games.
“But today we’ve scored three, could have scored a couple more, and the spirit and commitment of the players is there for all to see and has been for a while now.”
Bowen opened the scoring after just six minutes when he collected Fraizer Campbell's lay-off and cut inside Joel Lynch before shooting past keeper Joe Lumley from just inside the penalty area.
Worse followed for the home side in the 22nd minute, when Henriksen was allowed to flick Bowen's right-wing corner into the net from close range - the Norwegian's first goal of the season.
Polish winger Wszolek hit back less than two minutes later by finishing off a lovely Rangers move.
After nice link-up play involving Massimo Luongo and Nahki Wells, Angel Rangel threaded a pass through to Wszolek, who slotted the ball between keeper David Marshall's legs.
The home side were galvanised by their goal but continued to look vulnerable at the back.
They had a lucky escape when Grosicki breezed past Rangel and crossed from the left to an unmarked Jackson Irvine, who headed over.
Nevertheless, QPR were unfortunate not to be level by the interval.
Marshall kept them at bay with two fine saves, diving to his left to keep out Wells' low shot and later palming away Lynch's header from Freeman's corner.
And veteran full-back Rangel, who scored twice at Stoke last weekend, rattled the post with a volley after Hull had only half-cleared another Freeman corner.
A second-half onslaught from QPR seemed certain, but it never materialised.
McClaren sent Hemed on just after the hour mark in an attempt to breathe new life in to his team.
But the on-loan Brighton striker was unable to connect with Jake Bidwell's left-wing cross and dragged a shot well wide as Rangers continued to struggle.
McClaren took a risk by bringing on Hemed for Geoff Cameron, who had been performing an important role in front of a fragile-looking back four.
Six minutes after the change, Hull carved QPR open with ease and helped themselves to a third goal.
Bowen was sent through on goal by Grosicki and tucked away the loose ball after his first effort had been saved by Lumley.
Hull were then comfortable until Freeman netted his second goal in as many games before going close with a free-kick in the final seconds.