Vaccari went over to give the Dragons an early advantage
Second-placed Warrington's Super League title bid took a knock after a surprise defeat at bottom side Catalans Dragons.
The French side led 16-6 with two minutes to go in the opening half but tries from Chris Hicks and Jon Clarke made it 16-16 at the interval.
Two tries in two minutes early in the second half saw the Dragons move clear.
Brent Sherwin's 64th minute drop-goal then edged the home side 29-22 ahead although a Lee Briers converted try ensured a tense finale.
It means the Wolves remain four points behind league leaders Wigan with four regular season games to go.
Catalans coach Kevin Walters said:
"I'm happy with our performance today, we did some good things, there were a couple of times in the first half that we were soft in defence, but generally I thought it was a great effort from the guys.
"They responded very nicely from some harsh, and probably deserved criticism from many quarters after last week's performance.
"We have managed to get a result and performance tonight and it means a lot to us given our tally and where we are in the table and every week does count."
Warrington coach Tony Smith said:
"We started a bit flat today, and I thought our opponents outplayed us today and deserved their win, they showed great desire.
"We were behind the eight ball today from the start but we'll go away and lick our wounds and come back stronger for it.
"It doesn't matter who beats us, we won't sulk about it, we get ready for our next game and we'll turn our attention to Saints after we review this game.
"We'll go through the process in the same way as if we had won tonight. I'm sure the boys will be ready for Saints next week."
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