The hosts led by six points at the break with tries from Jack Buchanan and Joe Mellor, after Jack Hughes had put Wire in front early on.
Lloyd White's penalty extended the Vikings' lead, but Tom Lineham's try cut the deficit to four points.
The visitors dominated from then on, as tries from Declan Patton, Matty Russell and Peta Hiku secured victory.
Widnes coach Denis Betts:
"It was a really tough game and a tough contest until the point where we let them get back into the arm wrestle.
"We need to take opportunities when they present themselves and if we do that then it looks like a different game.
"Overall it was a good contest and one in which we competed throughout, but we made two errors and they have punished us. A side like Warrington can hurt you."
Warrington boss Tony Smith:
"There were two teams out there fighting for their lives and it showed.
"It's very important to get the series off to a winning start and both teams showed how important this is.
"Widnes had a real crack - it was the best I've seen of Widnes for weeks. They really took it to us. But we have to shown character and patience to get past them."
Widnes: Hanbury; Marsh, Bridge, Runciman, Thompson; Mellor, Craven; Buchanan, White, Dudson, Houston, Whitley, Cahill.
Replacements: Manuokafoa, Chapelhow, Olbison, Johnstone.
Warrington: Ratchford; Russell, Hiku, Atkins, Lineham; Brown, Patton; Hill, Clark, Sims, Jullien, Hughes, Cooper.
Replacements: King, Savelio, Philbin, Smith.
Referee: Phil Bentham (RFL)
Warrington came from behind to earn a hard-fought local derby win at Widnes in the first game of the Qualifiers.