The Giants had hoped to demonstrate their trophy-winning credentials by completing a double over the Warriors but a defeat by seven tries to two suggests they still have much to do to win over the doubters.
Josh Charnley had an off day with the boot, missing all four kicks at goal, but he scored two first-half tries to take his tally for the season to 18, seven in front of his nearest rival, to ensure Wigan enter the second half of the season in pole position.
Huddersfield, who won 20-16 at the DW Stadium in the opening round back in February, were well in the game at 12-12 early in the second half but the visitors adapted better to wet conditions and finished the stronger side.
The Giants demonstrated their attacking flair from the kick-off, with Scott Grix gathering Danny Brough's chip over the Wigan defence to get centre Leroy Cudjoe haring away but the final pass to Jermaine McGillvary went astray.
Thomas Leuluai's superb kicks forced two goal-line drop-outs but the Giants showed why they have the best defence in the league by holding the visitors out and they went in front after 14 minutes. Luke Robinson's dart from dummy-half caught the Warriors by surprise and Cudjoe's quick pass gave McGillvary the chance to demonstrate clinical finishing at the corner.
Brough had earlier missed a long-range penalty kick at goal but he made amends with a touchline conversion to make it 6-0 and the Yorkshiremen were good value for their lead.
But Wigan gradually came into the game and turned around 12-6 in front after scoring three tries in the second quarter. Quick hands from Michael McIlorum, Leuluai, Sam Tomkins and Darrell Goulding got Charnley over for his first before Tomkins brushed off Grix's attempted tackle to touch down for his 11th of the campaign.
Charnley took Goulding's pass to slide over for his second try, but Huddersfield drew level six minutes into the second half. Full-back Greg Eden took Grix's inside pass but he ghosted through the Wigan defence for his side's second try, which Brough goaled. The visitors were back in front when Eden dropped Brett Finch's kick, allowing George Carmont to score.
Liam Farrell fended off Kevin Brown to score Wigan's fifth try after 53 minutes. Tomkins added the extras to put his side 10 points clear and Carmont made no mistake moments later after more good work from Hock. Wigan had the final say when prop Jeff Lima forced his way over for his side's seventh, with Tomkins kicking his second goal.
The Reds trailed 20-16 until Broughton took a Luke Patten pass to go over in the corner but Daniel Holdsworth missed the conversion. Karl Pryce bagged a hat-trick for the Bulls, who were also awarded a controversial Tom Burgess try by referee Richard Silverwood.
Shaun Ainscough looked yards offside when he collected Ben Jeffries' kick to put Burgess over and Luke Gale converted to make it 20-16, but Broughton struck back after Oliver Elima was sin-binned.
Bradford went into the clash having triumphed in 22 of their 29 Super League meetings against Salford, who won 38-18 at Odsal in March.
Reds prop Adam Sidlow tore into the Bulls from the start and ploughed over for his first try since last June in the sixth minute after Craig Kopczak conceded a penalty. Holdsworth tagged on the conversion but the Bulls almost replied when Hargreaves released the ball close to the Reds line but the chance went begging.
Burgess made an immediate impression when he appeared as sub but Salford's defence held firm until Pryce powered over in the corner after 32 minutes. Gale missed the conversion but a surging Elliott Whitehead run gave Bradford more confidence.
Pryce notched his second try in three minutes from a looping Gale pass after Salford conceded another penalty. Gale made no mistake with the goal attempt to fire his side ahead 10-6 at the interval.
Sean Gleeson spilled the ball straight from the kick-off in the second half before Salford rallied courtesy of a sizzling Luke Patten break. Holdsworth and Gleeson combined for Danny Williams to squeeze over in the corner and make it 10-10.
The Bulls hit back immediately with Pryce completing his hat-trick after Jeffries saw the Reds cover out of position and his precision kick bounced kindly for the winger. It was still anybody's game and Gleeson's smart flick pass put Williams over for his second try after 55 minutes, with Holdsworth's conversion edging the Reds in front 16-14.
Pryce came close to a fourth try from a Gale kick but was pushed into touch by Williams. Both sides made frequent handling mistakes round the ruck but it was Burgess' controversial try nine minutes from time which restored the Bulls' lead, before Broughton's try ensured the points were shared.