Hull won the battle of Super League's big under-achievers to leapfrog neighbours Hull KR in the table and pile the pressure on struggling Salford.
The Reds dominated the second half of the match at The Willows but paid for a dismal 23-minute spell in which they conceded four tries.
They also leaked two more tries in the last two minutes of the match to go down to their seventh defeat of the season and remain just a point above bottom club Huddersfield.
Their misery was compounded by another injury to skipper Malcolm Alker, who made his comeback from torn knee medial ligaments 21 minutes into the game but was forced off again 12 minutes later.
Salford were never out of the top six last season but they will sink to the foot of the table if the Giants beat Wigan on Sunday yet they made the best possible start with two tries in the first six minutes.
Smart passing by Luke Robinson and Ian Sibbit created a two-on-one for centre Aaron Moule to exploit after just four minutes and Hull had barely recovered from the shock when a blunder by full-back Shaun Briscoe gifted the Reds a second try.
Briscoe waited for Robinson's kick on the last tackle to roll dead but it took a wicked bounce and Salford stand-off Luke Dorn followed up to dive onto the ball.
John Wilshere added both conversions to put his side 12-0 ahead but a needless penalty conceded by Michael Korkidas, who was placed on report for use of the elbow, put Hull onto the attack and they turned the game on its head with three tries in 14 minutes.
A neat offload by prop Paul King set up the position for scrum-half Richard Horne to combine with Kirk Yeaman to get winger Gareth Raynor over at the corner on 11 minutes for the first of his two tries.
Stand-off Paul Cooke, sorely missed during his absence with a hamstring injury, demonstrated his class when jinking over for a solo try and Hull edged in front on 23 minutes when centre Sid Domic punished a handling error by Gareth Haggerty to send winger Matt Sing racing under the posts.
Cooke added two of the conversions to make it 16-12 and it got even better for the visitors six minutes before half-time when loose forward Danny Tickle raced onto a clever grubber kick from Cooke.
Salford were grateful for the half-time whistle and the chance to regroup for the second half.
A flurry of penalties enabled them to make all the running at the start of the second half and they made the pressure pay on 46 minutes when Robinson lofted the ball to the wing, where Wilshere collected to race in for the Reds' third try.
The former Warrington winger added the touchline conversion to maintain his 100% record with the boot and cut the deficit to just four points but that was as good as it got for the home side.
Salford looked a different team, with Robinson causing Hull all sorts of problems with his tricky footwork and skilful ball distribution, and they tightened their defence to keep Hull pinned inside their own half for most of the third quarter.
On a rare foray into the Salford 20-metre area, Haggerty was placed on report for a high tackle on Hull's Scott Wheeldon and Cooke gave his side additional breathing space with an easy penalty goal.
As Salford pressed for an equaliser, Kevin McGuinness was brought down inches short by Briscoe and Stuart Littler was held up over the line but there was no way back once Horne landed a drop-goal four minutes from the end to put the visitors two scores ahead.
And Hull piled on the agony in the closing stages as Horne and then Raynor made light of some tired tackling to add further tries, with Cooke taking his goal tally to five.