Daniel Holdsworth capped a top display with three goals and a drop goal
Salford turned in a dominant second-half performance to earn only their second Super League win of the season.
Tries from Sean Long, Kirk Yeaman and Epalahame Lauaki had earned Hull a 16-12 lead at the break.
But Salford fought back to level at 20-20 thanks to two tries from Karl Fitpatrick to add to earlier efforts Adam Sidlow and Jodie Broughton.
Broughton then crossed again and Daniel Holdsworth added a touchline conversion before sealing it with a drop goal.
Teenage Hull winger Reece Lyne, in great form for the Under 20s this term, scored on his first start.
But that was small consolation for Richard Agar's side.
Without Richard Horne, Mark Calderwood and Peter Cusack, they suffered only their third defeat of the season, missing a chance to climb to third in the table.
Salford, still without suspended scrum half Jeremy Smith, brought back former Kiwi international Willie Talau in the centre and dropped Stefan Ratchford.
And they made a good start when scrum-half Holdsworth sent Sidlow stretching over for a third minute try.
Hull were back on level terms after 14 minutes when Long's kick rebounded kindly for the former St Helens scrum-half to touch down for his third try since his close-season move.
Holdsworth then put Steve Tyrer clear to set up Fitzpatrick's firsdt try.
But Stuart Littler's high tackle allowed Yeaman to outjump two defenders from Long's kick to cut the deficit to two points. And Hull went ahead for the first time when Lauaki's strength took him over, Danny Tickle's conversion earning a 16-12 half-time lead.
But Salford equalised straight after the restart when Broughton crossing in the corner from Talau's smart pass. And they went back in front, 20-16, when Holdsworth's kick looked to be heading out of play until cleverly tapped back by Tyrer for Fitzpatrick to bag his second try.
Lyne then celebrated his touchdown from Richard Whiting's pass to level again on the hour.
But the see-saw finally tilted Salford's way for the last time when Broughton went over for his second try in the corner.
That was brilliantly converted by Holdsworth, who was not finished, clinching victory with that drop in the dying seconds.
Salford coach Shaun McRae:
"We were impatient at times in the first half and deserved to be down.
"But we had a 100% completion rate in the second half and that was the first time in my coaching career I have seen that.
"It was a big turnaround from last week when we let ourselves down at Wakefield and we showed what we can do."
Hull coach Richard Agar: "It was probably as bad as we have been all year and we were very ordinary.
"Our discipline with the ball was poor and we gave away some cheap penalties which were a contributory factor.
"If we want to be title challengers, performances like this have to be few and far between and we need to fix things up urgently."
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