Bowen coolly converted to register his third goal of the campaign after Daniel Ayala was penalised for a needless shove just inside the box on Chris Martin.
It was a deserved point for the Tigers, who had fallen behind six minutes into the second period after Britt Assombalonga steered the ball home from close range following Jonny Howson's cross - for his fourth strike of the season.
Opting to field a bold 3-4-3 formation, with Kamil Grosicki brought in for his first start since April 28, Hull had the better of a scrappy first half against their high-flying rivals.
An early chance saw Bowen nod over following's Grosicki centre, with the Polish winger seeing plenty of the ball in the first half.
A positive start from the Tigers was almost crowned by a tenth-minute opener with a quickly-taken free-kick finding its way to captain Markus Henriksen, whose drilled shot flashed just wide.
It was a half in which both keepers were not overly extended, with Boro's best moment coming in the 20th minute when Britt Assombalonga - starting up front in the league alongside Jordan Hugill for the first time - steering an angled shot wide of the far post after being supplied by his strike partner.
After a quiet first period, the visitors produced the first meaningful foray on the resumption when enterprise from George Friend saw him cut inside before unleashing a drive which flew narrowly over.
The breakthrough then arrived for Boro as Hull were caught napping at the back, with their defence switching off following Howson's cross on the right and the alert Assombalonga, left unmarked at the far post, prodded the ball home from close range.
The striker was soon presented with another chance as Boro suddenly scented blood, but his curler was straight at David Marshall.
Challenged to produce a response, Hull showed appetite, but struggled to trouble Darren Randolph.
One decent opportunity did arrive with the ball breaking nicely for Bowen, but his curler flew wide when he was well placed.
Boro then went close to sealing it when Flint's header flew inches over following an exorcet of a long throw from Ryan Shotton.
Randolph was then forced into his first meaningful wide with the keeper grasping a well-struck free-kick from Grosicki.
Hull were then handed a lifeline after Ayala's indiscretion with Bowen calmly sending Randolph the wrong way from the spot.
The game was back in the melting pot and the hosts applied pressure in their quest for a winner.
But it was Boro who went the closest with Marshall showing his mettle to make a fine save to turn away a late downward header from Howson following an inviting centre from substitute Stewart Downing.
Hull City: Marshall, Burke, Elphick, De Wijs (Kingsley 33); Kane, Henriksen, Irvine, Lichaj; Bowen, Martin, Grosicki (Campbell 76). Substitutes unused: Long, Stewart, Dicko, Keane, McKenzie.
Middlesbrough: Randolph; Ayala, Flint, Friend; Shotton, Clayton (Besic 76), Saville, Howson, McQueen (Downing 76); Assombalonga, Hugill (Braithwaite 76). Substitutes unused: Dimi, Batth, Fry, McNair.
Referee: D England.