A first try for over two years from the former Great Britain prop Stuart Fielden was the vital score as Wigan remained on course for Wembley at the end of a Challenge Cup tie they seemed at times intent upon losing.
Fielden took a pass from Tim Smith in the 63rd minute and beat three defenders for what was anything but a typical prop forward's try.
"People say a lot about Stuart Fielden, but his form over the last month has been pretty good," said his coach, Brian Noble. "He is the consummate professional."
The try, which wiped out a one-point Wakefield lead, was followed by one from Sam Tomkins, who took Michael McIlorum's pass and threw a huge side-step. But it was Fielden who had made the crucial break-through that helped Wigan become the first club into the quarter-finals.
They had spent most of the first half repairing the self-inflicted damage of the first few minutes. They could hardly have made a worse start, allowing Danny Brough's kick-off to run dead and then coughing up possession through Fielden's fumble. Wakefield made them pay when Brough's pass found Jason Demetriou and the Wildcats' captain handed-off George Carmont with surprising ease.
Pat Richards put his kick-off straight out and Wakefield took their lead into double figures when Tevita Leo-Latu scored. Richards then had a try disallowed for ball-stealing before Wigan launched their fightback, the try credited to Carmont despite an apparent forward pass from Sean O'Loughlin.
McIlorum then got the try that brought them level, before Brough made the curious decision to drop a goal and edge his side back in front.
A fine break by O'Loughlin set up Phelps, but Wigan were mistake-prone again at the start of the second half and Brough, who had apparently run into a blind alley, pushed through a little kick which sat up perfectly for Tony Martin. The stage was thus set for Fielden, although Noble was full of praise for the way his whole side had "rolled their sleeves up" after their dreadful start. "They made it very hard for us," he said of Wakefield. "But they're a tough, scrappy team."
The Challenge Cup holds a special place in the Wigan psyche, but Noble refused to be drawn on whether this side had "Wembley written all over it."
"All I know if that it has 'quarter-final' written all over it," he said.
Wakefield: Blaymire; Grix, Demetriou, Atkins, Petersen; Martin, Brough; Wilkes, Obst, Moore, Snitch, Pitts, Leo-Latu. Substitutes used: Drew, Bibb, Sculthorpe, Winterstein
Wigan: Phelps; Roberts, Gleeson, Carmont, Richards; Smith, Leuluai; Fielden, McIlorum, Coley, Bailey, Hock, O'Loughlin. Substitutes used: J Tomkins, S Tomkins, Paleaaesina, Prescott.
Referee: P Bentham (Warrington).