The victory - only the Bulls' second in 11 games - leaves them a point adrift of Wakefield and two behind the eighth-placed Black and Whites. Cummins said: "The players have shown a lot of heart, especially as we were down two players, having lost John Bateman (ankle) in the first half and Tom Olbison (knee) in the second.
"It wasn't pretty but we got the job done. We found ourselves stuck in our own 20 metres for what seemed like two weeks in the second half and we had to find a way to win the game.
"When you have a bad run you sometimes try and play things a little too safe. We have players who can take people on and they need them to do it. But that fight is there and they showed it tonight."
Cummins praised huge Kiwi prop Manase Manuokafoa, who was a massive presence in all senses, adding: "Nas has got the size and he's getting a bit more game time - I thought he was great against Wigan. The other week too - he really battered them."
Hull have now lost five league games on the trot and coach Peter Gentle reflected on an epic Tetley's Challenge Cup win in the south of France last week and having played four games 19 days.
He admitted: "We had plenty of ball in the second half but the execution wasn't there - maybe it's fatigue? We were brain dead at times and your head is the always the first thing to go when you are fatigued. It was an opportunity for us to get our season back on track but we missed it."
Hull made the best start and went ahead through a Tom Briscoe try after 12 minutes. Danny Tickle converted but Bradford hit back with two quick-fire scores from Jarrod Sammut, returning after seven weeks out through injury, and Elliot Kear to lead 12-6 at the break.
Hull levelled when Tickle converted his own try after the interval and bossed much of the second half, only to be frustrated by some tenacious Bulls defence.
Then, with five minutes to go, Sammut dropped a goal to edge the home side a point ahead and in the closing seconds Matt Diskin muscled his way over and Jamie Foster landed his third conversion to ensure an end to the Bulls' long win-less run.
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- Tom Olbison