Bowen sent Chris Maxwell the wrong way in the 85th minute after striker Chris Martin had been shoved to the ground by central defender Jordan Storey.
Preston struck back in stoppage time, however, as substitute Louis Moult spun off Eric Lichaj and fired home from 12 yards after a cross from Darnell Fisher.
It gave the visitors a point against the side they had left bottom of the table before the international break by virtue of a 4-0 win against Wigan.
Hull, who saw the ball strike the woodwork three times, were inspired by Kamil Grosicki in the second half but that elusive win would not come.Injury ruled out Tigers captain and midfield man Markus Henriksen for the first time in the Championship but attacking duo Bowen and Grosicki were restored to the starting line-up with on-loan Derby striker Martin leading the line.
Fellow forward Fraizer Campbell recovered sufficiently from the groin trouble which forced him off in the 1-0 defeat at Sheffield United to earn a place on the bench and central defender Jordy de Wijs returned to the starting line-up after an ankle injury.
Preston's Irish international striker Sean Maguire made his first start of the season after three months out with a hamstring problem. Ben Davies was also back after hamstring trouble and Ryan Ledson had shaken off an ankle problem to replace the suspended Ben Pearson in midfield but central defender Tom Clarke was ruled out by injury.
Preston did much of the early pressing and Jackson Irvine was booked for a late challenge but the Tigers won the first corner, which was delayed for treatment to Tommy Elphick.
They almost took a 33rd-minute lead when Irvine sent Grosicki down the left channel and he squared for supporting centre-back Reece Burke to smash a long-range drive against Chris Maxwell's right-hand post.
Martin also went close when he headed a deflected cross from the right from Daniel Batty against the bar.
Burke and Elphick required treatment after a clash of heads on the corner of their area - the former requiring a head bandage ahead of five minutes of stoppage time.
Eric Lichaj had a great chance to send the Tigers in ahead but he hit over from eight yards after being teed up by Martin's knock-down from Batty's cross.
Neither side made a change at the break and Hull created the first chance, Grosicki going down the left and cutting the ball back for Bowen to see his eight-yard attempt kept out by Maxwell's legs as he went the wrong way.
Grosicki forced a flying save from Maxwell but two successive corners brought Hull no reward.
The Tigers were again out of luck as Irvine chipped the ball through, Bowen knocked it towards goal and Maxwell's hand diverted it onto the head of central defender Jordan Storey, who was relieved as the ball cannoned back off the post before being cleared for a corner.
There was a minute's applause in the 76th minute for former Hull player Charlie Crickmore (1942-2018), who passed away recently.
Preston almost struck in the 79th minute but David Marshall pushed over substitute Paul Gallagher's looping header from Alan Browne's cross.
Hull would not be denied and Bowen kept cool to fire the penalty into the roof of the net after Martin had been impeded.
More drama followed in the five minutes of stoppage time, however, as Moult rescued a point for the visitors.
Adkins said afterwards: "I think we played well and created a lot of chances. It was a good, good performance.
"We put ourselves in a position to win it and it was just a case of seeing the game out.
"We've created a lot of chances, which is important, and it was another good performance.
"It's just fine margins - we've hit the woodwork three times and their goalkeeper has made a lot of good saves.
"The players are working hard. We've got a point and we've got to keep going."
Preston are outside the relegation zone on goal difference, but Neil was happy with a point.
He said: "I thought we started the game quite brightly, but from 15 minutes onwards I thought Hull were better.
"We didn't keep the ball in the top end of the pitch well enough.
"We rode our luck a little bit. We made a few changes and I thought we were on top when they scored.
"It was quite a strange game. They had the most of the territory and the best of the clear-cut opportunities, but we also had chances.
"To be fair to Hull, they were really brave, but I think we defended relatively well.
"I still wasn't that pleased with how we've played, but, based on the game, we'll take a point and move on to the next one.
"It's a nice stat to go unbeaten three games at this level."
On the penalty, Neil said: "I thought it was a bit soft - I don't think Chris Martin was getting the ball - but I've no complaints and no qualms about it."