Craig Hall put the Wildcats ahead with a try after just 40 seconds, but once Wigan took the lead they never lost it and scored seven tries in total.
Wakefield only trailed 24-18 at half-time but missed chances to cut the gap.
And with Matty Smith scoring all of his six conversions, the visitors secured their first away win of the season.
It was the Warriors' third successive win and a ninth consecutive defeat for bottom-of-the-table Wakefield, who improved dramatically from the 80-0 drubbing by Warrington in their last Super League match.
The hosts made a dramatic start as Matt Ryan raced clear to set up a try for Hall, who also kicked the conversion.
The lead lasted only seven minutes until Dom Crosby scored his first try for more than two years and Smith made it 6-6 with the conversion.
Before the break, Wigan took control with further tries from Burgess and Dom Manfredi but replies from skipper Danny Kirmond and Pita Godinet, in his first start of 2015, kept Wakefield in touch.
Among all the tries, there were yellow cards for Wigan's Sam Powell and Tim Smith of Wakefield, who squared up to each other.
Dan Sarginson set up Burgess straight after the interval and his converted try gave Wigan a 12-point cushion for the third time in the evening.
But Godinet capitalised on an error by Taulima Tautai to set up Chris Riley to give the Wildcats hope.
However, Lee Mossop went over before Burgess completed his treble to wrap up the points.
To complete Wakefield's misery, they lost debutant Jordan Crowther, prop Ian Kirke and loose forward Danny Washbrook during the match.
Wakefield coach James Webster: "We definitely didn't get beaten on effort. We tried to get a foothold in the game but came up with crucial errors at crucial times.
"Even though we scored some points, we didn't build pressure, we never sat on their try-line. But it's a good learning curve for us.
"I came here looking for improvement and I got that. If we get the same improvement next week, we might get Saints.
Wigan coach Shaun Wane: "It was just a win. Defensively we were poor . We were decent with the ball but I'm a bit frustrated we weren't patient in the final third.
"It's not an easy place to come - St Helens only won by four - I've been coming here since 2010 and I've never given a positive talk in the dressing room afterwards.
"But I still expect a better performance than that. Mentally we just weren't there today. The positive is that we found a way to win."
Wakefield: Hall, Owen, Ryan, Lyne, Riley, Godinet, T. Smith, Scruton, McShane, Kavanagh, Washbrook, Kirmond, Crowther.
Replacements: Lauitiiti for McShane (33), Kirke for Kavanagh (29), Simon for Crowther (17), Scruton for Simon (50).
Substitutes: D. Smith.
Sin Bin: T. Smith (34).
Wigan: Hampshire, Manfredi, Gelling, Sarginson, Burgess, Williams, Smith, Mossop, McIlorum, Crosby, J. Tomkins, L. Farrell, Bateman.
Replacements: Clubb for Mossop (21), Powell for McIlorum (28), Flower for Crosby (19), Tautai for Bateman (30).
Sin Bin: Powell (34).
Att: 3,107
Ref: Robert Hicks (RFL).
Joe Burgess scored his first Super League hat-trick as Wigan survived an early scare to beat Wakefield and move up to second in the table.