The prolific winger scored at the start and end of the first half but goals in the final half an hour from Josh Scowen and Tomer Hemed meant the points were shared.
Bowen scored with two almost identical shots, cutting in from the left to fire home, but Hull's bid for a Sky Bet Championship play-off spot suffered a late blow.
QPR manager Steve McClaren had warned his players they were in a relegation scrap following defeat to Rotherham last time out and they responded well after going two goals behind.
Scowen got the visitors back into the game just after the hour with a scuffed effort which rolled into the corner of the goal before Hemed's persistence saw him snatch the draw.
Bowen raced through onto a ball over the top and his low shot forced Joe Lumley to get down low to his right before the goalkeeper claimed the ball at the second attempt with five minutes gone.
But he could not deny Bowen a minute later as the winger cut inside Jake Bidwell from Kamil Grosicki's pass and fired low into the opposite corner of the goal for his 20th of the campaign.
Bidwell nearly made up for that when he was set up by Ebere Eze but hit his shot wide of the far post.
Geoff Cameron headed wide from a corner as QPR tried to get back into a game which Hull continued to largely dominate.
David Marshall beat away a shot from Luke Freeman as QPR pressed for a response.
Eze hit a low ball from the left but Stephen Kingsley got in an important block to deny Nahki Wells as the forward looked to get a telling touch from close range.
Robbie McKenzie saw a shot blocked from distance as Hull threatened three times in the same attack eight minutes before half-time.
Bowen scored his second just before the break, collecting a ball from Grosicki to the far post before cutting inside his marker again and repeating his shot across goal, if this time from a shorter distance.
Massimo Luongo should have done better when he stuck a foot out to Freeman's low cross but only diverted the ball over the crossbar from eight yards.
Hull nearly grabbed a third just before the hour but for once Bowen fluffed his lines.
The winger completely missed his kick but the ball fell to Fraizer Campbell whose shot was blocked on the line by Joel Lynch.
QPR were back in the game shortly afterwards as substitute Scowen beat Marshall with a scuffed effort into the corner.
Reece Burke did well to block a shot from Wells and from the resulting corner Marc Pugh headed off the line from Scowen.
Just as it looked like Hull had done enough to secure the win, QPR equalised with six minutes to go.
Substitute Hemed poked home from close range four minutes after coming on after Scowen had cut the ball back to ensure the points were shared.
"We had said before the game how important it was to go and win it," added Nigel Adkins.
"The first goal it should have been a free-kick in the build-up. He side-foots it in from 35 yards and we have got to stop that.
"The second goal, the ball has gone out but the linesman can't see it because he is not up with play. Our centre-half is appealing for it and their player scores.
"I am so frustrated that we put ourselves in a position to win the game and we have only got a point."
R's boss Steve McClaren said: "That was huge! We beat Leeds two weeks ago and I thought that result was a turning point.
"We have been disappointing in the last three games. After being beaten with the last header of the game on Wednesday, on Thursday it was very difficult to get any work or lift the players. Friday they were very good, a good response with lots of energy."