Oliver Gildart crowned a stirring comeback to claim a nailbiting 28-26 victory, having trailed 26-12 midway through the second-half.
The Warriors only flipped the game to Widnes with nine-hours notice, having previously postponed their home match because of the pitch problems at the DW Stadium.
The saga has cost Wigan a “significant” sum and they face an RFL investigation into the embarrassment - which came just days after their epic World Club Challenge win.
“We have a mentality of ‘any time, any place’, and I told the players to be ready to play,” said Wane. “I was told (on Thursday) the game was off, but something might be sorted.”
He didn’t comment on the decision itself, saying his role is “to coach the players.”
“The main objective was to come to a tough place and get the win, it was always going to be a tough ask,” he continued.
“I know what the players have been through, I’ve every respect for Widnes, they played outstandingly well and I couldn’t have moaned if we lost the game.”
Widnes coach Denis Betts admitted it was a “bizarre situation” but didn’t use it as an excuse for their late collapse.
“The club has done well to put a game on at such short notice,” said Betts. “I said yesterday, I can’t control it, don’t get emotional - but we needed to play, if it had been postponed it would have been one game in a month.
“You can look at it two ways; we had a fantastic game, or say these things shouldn’t happen.”
Wigan were watched by a packed away stand of around 2,000 fans, and the players showed their gratitude by throwing their match shirts into the crowd after full-time.
Meanwhile, Wane says Jake Shorrocks will have a knee injury scanned today but hopes it is not as bad as first feared.