The Vikings looked set for only a third win this season when tries from Chris Houston, Rhys Hanbury and two from Patrick Ah Van opened up a big lead.
But Jansin Turgut got a try back for Hull 30 seconds before the break.
Full-back Jamie Shaul got two of Hull's five unanswered second-half tries, with Carlos Tuimavave, Albert Kelly and Danny Washbrook also crossing.
A fourth successive win for Lee Radford's side, in which Marc Sneyd added four conversions and a drop goal, lifted them back to second in the Super League table.
Widnes, already without the injured Corey Thompson, who announced on Thursday that he will leave at the end of the season, lost centre Chris Bridge after just 90 seconds.
But scrum-half Tom Gilmore, who also converted three of their four tries, was the inspiration behind their first-half show.
Two tries in two minutes either side of the break, the second from Shaul triggered by Josh Griffin's half-time arrival, proved the turning point for Hull.
Tuimavave was put over for try number three by a deft pass from stand-off Kelly, who then found a gaping hole to romp in from 50 metres for his 12th try of the season, Sneyd adding the extras to level the scores with 15 minutes left.
Shaul then crossed for his second with a typical bursting effort as Widnes' defenders ran out of energy, and Sneyd dropped the goal which left Widnes needing two scores before Washbrook had the final say with a simple score.
Widnes head coach Denis Betts told BBC Radio Merseyside:
"If we had points for winning halves, we'd be in a lot better position. These past few weeks we've won the first halves in games but not got anything out of them.
"It was the best 40 minutes of the year for us. Then we stopped doing everything. Our shape dropped, our talk dropped off. We had a great lead and energy but then don't turn up in the second half.
"They have got some good players, Jamie Shaul, Albert Kelly, Marc Sneyd, Carlos Tuimavave, but we let them back in. We were chasing shadows.
"Chris Bridge knocked himself out in the tackle. He had his head slammed to the ground and he's still a bit dazed. That means we had one rotation less. We looked really tired in the second half and it showed."
Hull FC boss Lee Radford told BBC Radio Humberside:
"We gave ourselves a really difficult job to do because of the start we made. But we scored before the break and that gave us a chance. And we could have made it even easier in the end as we bombed some chances.
"We were out-enthused in every department in the first half. We showed the lads some clips at half-time why we were in the situation we were in.
"We needed something more and we needed some energy and we eventually got it. We wanted to get Albert Kelly carrying the ball a bit more and he managed to do that.
"The group know comebacks like that are possible but we don't want to be doing that. We want to be on the front foot from the off."
Widnes: Hanbury; Marsh, Bridge, Runciman, Ah Van; Mellor, Gilmore; Dudson, Heremaia, Buchanan, Houston, Dean, Cahill.
Replacements: Whitley, O'Carroll, Gerrard, D Walker.
Hull: Shaul; Fonua, Connor, Tuimavave, Michaels; Kelly, Sneyd; Green, Houghton, Watts, Washbrook, Minichiello, Thompson.
Replacements: Bowden, Fash, Griffin, Turgut.
Attendance: 5,082.
Referee: Gareth Hewer.

Molloy has made 40 appearances for the Wildcats since joining from Huddersfield in April 2013.
Meanwhile, centre Bill Tupou will also miss Saturday's Challenge Cup semi-final at Warrington after suffering a minor tear in his hamstring.
"The injuries are a loss but we've got depth in the squad," head coach Chris Chester told BBC Radio Leeds.
Hull FC produced one of the comebacks of the season as they hit back from 22-0 down to win at bottom club Widnes.
[NEXT_CONCEPT]
Wakefield Wildcats second-row forward Jon Molloy will be out for four weeks after suffering a torn pectoral muscle.