The Giants remain sixth in Super League but will still be harbouring hopes of breaking into the top four by the end of the season.
With four games remaining and clashes with St Helens and Warrington to come, head coach Paul Anderson and his troops have their fate in their own hands.
However, Anderson will want more complete performances than this derby win, in which the Giants were in control only to lose the plot a little in the second half.
The Giants had Shaun Lunt back at hooker after two months out with a niggling calf injury and the visitors made the best of starts.
After Wakefield surrendered possession by putting the kick off straight into touch, the Giants made the most of their first set of six tackles with Luke Robinson and Danny Brough combining to send Joe Wardle over the line (with little over a minute on the clock).
While Brough missed the kick, although one touch judge initially flagged for a goal, he made no mistake 10 minutes later from in front of the sticks after Eorl Crabtree had powered over the line.
A sloppy pass from Wakefield hooker Paul McShane was snapped up by Jermaine McGillvary, but he was hauled down 20 yards short of the line.
The pressure was maintained on the Trinity line, however, and Lunt went over from a neat move and Brough added the goal.
It remained one-way traffic as the Giants looked capable of breaching the Wildcats line at will, and they made it 22 points in 27 minutes when Craig Kopczak battered his way over and Brough again added the goal.
The Giants next try was a gift as a Brough bomb was spilled by Wakefield full back Jarrod Sammut and Luke Robinson was on hand to flip the ball on and Kruse Leeming went in for his first try.
Wakefield finally looked as though they might trouble the scorers on 36 minutes, but the ball was lost five yards from the line and McGillvary snapped it up and went the length of the field to score.
Brough failed with the kick but the Giants were a very healthy 32-0 ahead at the interval.
Hopes of nilling their derby rivals vanished for the Giants when the home side made a much brighter start to the second half and exploited a gap on the left fringe of the visitors’ defence for Sammut to go over, and he added the goal.
Sammut and Ali Lauititi then looked to have sprung the Giants defence again but were pulled back for a forward pass, and the full back was beginning to pose real problems for the Giants as he was held up over the line.
The Wildcats managed to make something of their pressure when Paul Sykes nipped through at the posts and Sammut added the goal, but handling errors in their next two attacks robbed them of truly putting the Giants under the cosh.
Compared with their opening half effort, the Giants foot seemed to have come off the gas, but they managed to find a bit of extra zip going into the dying minutes.
A neat dabbed kick through from Brough looked to have put Brett Ferres in but the Wakefield defence held firm on the line.
The visitors did strike again as Jake Connor shot through to score but Brough put his kick wide of the mark.
Wakefield scored on the hooter as Sammut notched another try and added the goal.
But in the end it was the efforts of the first half that saw the Giants improve their hopes of a top-four finish, while Wakefield can now plan for next season without worrying about a flirtation with the play-offs.