With Nouha Dicko quickly adding to Bowen’s 32nd-minute opener, the Tigers were on top but substitute Aboubakar Kamara made it 2-1 with a 48th-minute penalty and equalised in the 85th minute.
With Kamil Grosicki out with an ankle injury, Bowen got his first start under Adkins, having damaged a knee in the 2-2 draw against Sheffield Wednesday and making his comeback from the bench in the last three games. This was the only change made by Adkins for his fifth game in charge after the goalless draw against Derby.
Striker Fraizer Campbell and Brazillian playmaker Evandro began their own comebacks from injury on the bench.
Fulham, led by former Tigers player Tom Cairney, arrived fresh from a 3-2 triumph at Cardiff City and on the back of five wins from their last seven Championship games.
It was a tame opening quarter with Fikayo Tomori grazing the bar from an offside position and Denis Odoi heading over his own bar from Jon Toral’s free-kick for the Tigers.
But it was the Tigers who took a 32nd-minute lead, Bowen poaching his 11th goal of the season from inside the six-yard area after Toral and Jackson Irvine had won headers from a corner.
It was soon 2-0 as Nouha Dicko burst onto a pass down the middle from Toral and went between two defenders before firing into the roof of the net.
Fulham then made two changes, Neeskens Kebano and Aboubakar Kamara replacing Floyd Ayite and Sheyi Ojo.
Kebano went close before the break, flicking a header narrowly wide after Toral had fired over at the other end.
Kamara put Fulham back in it when he won and converted a penalty following a needless trip on the corner of the area by Michael Hector as the striker sought support moving out of the danger zone after collecting a ball over the top from Cairney.
Kebano soon went close to equalising when he clipped over Allan McGregor but also the bar after bursting down the left channel.
Tigers made their first change in the 68th minute when Markus Henriksen replaced Kevin Stewart.
Toral was denied from close in by the legs of goalkeeper Marcus Bettinelli after Dicko’s shot had been deflected.
Campbell came on to acclaim as he replaced a tiring Toral in the 73rd minute.
McGregor took a blow to the head diving at the feet of Ryan Sessegnon - Kamara firing the follow-up over - but continued after treatment.
Dicko got an ovation as he was replaced by Max Clark before patient build-up play around the edge of the area conjured enough space for Kamara to place the ball inside McGregor’s left-hand post to make it 2-2 and claim a deserved point.
Hull could slip into the bottom three if they lose to relegation rivals Bolton on New Year’s Day, and manager Nigel Adkins has challenged his side to win 10 games in order to stay up.
“I thought the first half was exceptional,” he said. “We’ve gone 2-0 up, we could have been more.
“We started the second half well - their keeper made a good save from Nouha - and lo and behold one of our defenders has given a stupid penalty away and that changed the complexion of the game for me.
“We’ve got to go again because we play Bolton in 48 hours.
“You look at the league table and we need to get another 10 victories to make sure we’re in the division again next year.”