A relieved Brian Noble described Scott Naylor's last-gasp try as "freakish" and admitted the Bulls were lucky to leave Wilderspool with a victory.
Bradford cemented their second-place in Super League with a 24-20 victory over Paul Cullen's Wolves courtesy of a bizarre Naylor score with just seconds left.
Warrington's Dean Gaskell dived full length to stop a Paul Deacon 40/20 but succeeded only in knocking the ball into the path of Naylor to touch down.
The Bulls, missing Jimmy Lowes and Lesley Vainikolo, lacked their usual invention in attack and had to come back from behind three times for their hard-fought victory.
"Warrington proved they are very difficult to beat at home but the win was a reward for our effort and desire although there is still plenty of improvement in us," said Noble, whose side were six points behind with four minutes left before a Mike Forshaw try and Paul Deacon conversion evened things up ahead of Gaskell's gift to Naylor.
"We got a 40/20 set and the conclusion of it was a bit freakish. There was an element of luck in it.
"I thought we had real difficulty in establishing field position which is unusual for us and we didn't really trouble Warrington.
"Their defence was manful and they bashed us around a bit although the bounce of the ball went their way quite often.
"They are a very difficult team to beat but we were not up to our usual standards. But it was a great win for effort and desire."
Warrington coach Paul Cullen was disappointed that his side had failed to hang on for a famous win but did not blame Gaskell and was encouraged by the way they held their own against the Bulls.
"It was a fantastic game and we turned in a very professional performance but it wasn't professional enough," said an angry-looking Cullen after the game.
"We put the ball on the floor ten times and Dean Gaskell was no more responsible for this result than anyone else who made a mistake."
Meanwhile, fans are being urged to get their tickets early to avoid disappointment for the next two Bulls home games.
On Saturday Wigan come to Odsal and then St Helens arrive the following Friday with crowds in excess of 20,000 expected for both games.
"People should think about getting the tickets as soon as possible for these games," said a club spokesman.
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