The Wildcats trailed throughout the match but, after coming from 18-8 down to cut the deficit to two points, thought they had snatched victory when centre Lee Smith went over for a try, only to have it disallowed for a forward pass.
Huddersfield, who gave a debut to former Widnes forward Anthony Mullally, were generally the more impressive side but could never shake off their gritty opponents in a tense, scrappy affair at the Rapid Solicitors Stadium.
Danny Brough also kicked three goals for the Giants with Peter Fox, Lee Smith, and Ben Cockayne crossing for Wakefield and Paul Sykes booting two goals.
Wigan returned to winning ways following last weekend's defeat to Huddersfield after running riot in the second half as they beat London Broncos 48-18.
Iain Thornley and Josh Charnley went over in the opening 11 minutes but Sam Tomkins was sin-binned for 10 minutes for talking out of turn to the referee and that sparked the visitors into life as they responded with scores from Liam Colbon and Keiran Dixon to silence the DW Stadium crowd.
Michael McIlorum and Chad Randall traded scores and it looked like London would lead at the break but Warriors captain Sean O'Loughlin went over for the home side to lead 22-18 and five unanswered second-half tries saw the Warriors ease clear.
Thornley and Charnley both doubled their tallies after the break with Tomkins, Pat Richards and Blake Green also crossing.
Richards kicked six goals for Wigan with Michael Witt booting three for the Broncos.
Castleford could not end a forgettable week on a high note but a drop goal from Gareth O'Brien rescued a point in a 17-17 draw against Catalan Dragons at the Wish Communications Stadium.
The hosts, for whom chief executive Steve Ferres resigned due to differences with the club's board, trailed on three occasions but battled back to lead 16-12 with 15 minutes remaining.
However, Damien Blanch's try and a drop goal put the Dragons ahead by a single point but O'Brien ensured the spoils would be shared with a one-pointer of his own from 20 yards.
Jordan Thompson, Michael Shenton and Kirk Dixon scored the tries for Cas with Jamie Ellis booting two conversions.
Vincent Duport and Louis Anderson got the other tries for Catalan and Thomas Bosc kicked five points in total.
Danny Williams scored a late try as Salford beat Hull KR 38-34 to claim their first Super League win of the season.
Hull KR led 34-14 until the Reds rallied to score four converted tries without reply. Defeat was tough on Michael Dobson who piled up 18 points with two tries and five goals, but the Reds had the man of the match in Mark Sneyd.
Both sides finished with 12 men after Reds prop Lee Jewitt and Rovers forward Adam Walker were sent off after a punch-up.