The Warriors are currently struggling to qualify for the semi-finals as they currently sit sixth in the Super 8s table and face a crucial clash at arch rivals St Helens on Friday. Saints sit fifth. Both have 27 points, one behind fourth-placed Wakefield.
Williams was unable to add the goal and the game appeared to go away from the Warriors as Hull showed their class in the third quarter.
Centre Josh Griffin experienced the agony of losing his grip on the ball over the line but the pivotal moment came with a 40-20 kick from Sneyd that got the Black and Whites into the ideal attacking position.
Kelly made the most of it with a miracle pass out of the tackle and Fonua produced a spectacular one-handed finish to grab his second try, which was inevitably converted from the touchline by Sneyd to open up an eight-point lead.
Fonua thought he had a hat-trick on the hour only to have the try disallowed by video referee James Child - and that gave Wigan a reprieve.
Substitute forward Tony Clubb forced his way over from Williams' pass only to lose the ball, referee Phil Bentham ruling out a penalty try, and Wigan's last chance looked to have disappeared when Burgess sprinted up the touchline but was forced over the sidelines by full-back Jamie Shaul.
However, cut-out passes from O'Loughlin and Farrell got Burgess racing over for Wigan's third try to give them renewed hope, before last-minute celebrations were cut short when referee James Bentham correctly ruled out what might have been the winner.
Man of the match Marc Sneyd on how he responds to his critics: "I enjoy going home after a game and sitting on Twitter looking at a few people giving me stick.
"You give them a little favourite and can just imagine what they're like sat at home snapping while you're laughing your head off."
Hull coach Lee Radford on his team's performance: "It was a fantastic effort. I said at half-time these (Wigan) boys do not give in and it will go to the 80th minute. That's instilled in them from the coach (Shaun Wane) downwards and they did not disappoint.
"We had to fight for everything today. We went into our shell in the final 10 minutes, they put me on the edge of my seat, but it was a special effort, special supporters and a special club."
Radford on Sneyd's award: "I'm glad he's in our side. He's had a big impact on our club since he walked through the door.
"One thing that I admire about him most is the criticism he's had to receive playing that position at this club.
"If he's not winning people over now, I don't think he's ever going to."
Hull captain Gareth Ellis on winning ahead of his pending retirement: "A Challenge Cup win is special regardless, but obviously knowing I'll never get this opportunity to do it again, it's huge.
"It's huge for the club. We spoke about how we want to be consistently challenging for trophies and to win two on the bounce is massive.
"We've made history at the club."
Wigan boss Shaun Wane admitting his side were second best: "I thought we had a chance but I don't think we deserved it.
"I thought what we dished up in the second half was not good enough. We didn't put them under enough pressure in the second half. Quite rightly, they are the winners.
"We didn't do enough to win a game of this magnitude."