Jermaine McGillvary set up Lee Gaskell for Giants' first try, but Morgan Escare went over to level the scores.
Darnell McIntosh's try restored the visitors' lead, with Escare missing his kick after Tom Davies crossed on debut.
Danny Brough's two penalties and two conversions kept Giants ahead despite Anthony Gelling's try, but Escare's late penalty rescued the hosts a point.
The result ended Wigan's perfect start to the season, but Castleford's defeat by Salford means the World Series champions are now a point clear at the top of the table.
Giants move up to eighth in the table, with Brough's kicking taking him to ninth in the all-time Super League points chart.
The visitors had looked set to claim a third win of the season, but their hopes were dented when Kruise Leeming was sent to the sin-bin, with Escare kicking the final points of the game moments later.
Wigan head coach Shaun Wane told BBC Radio Manchester:
"I thought we were lucky to get away with it to be honest.
"What the players need to understand is when we have a bit of adversity like that not much changes with the way we attack, but we just felt a little bit sorry for ourselves.
"It was a dour game on a Sunday afternoon and the weather was poor. I think we fell into the trap and didn't lift ourselves."
Huddersfield head coach Rick Stone told BBC Radio Leeds:
"I think if we could have held our composure at the end we could have managed it.
"Obviously with Kruise getting sent to the sin-bin that didn't help our cause, but there was probably a few scenarios before that we could have managed a bit better.
"Hopefully we'll learn from it. We defended pretty well, scrambled hard for each other in the last 10 or 15 minutes, so hopefully we take some positives out of that."
Wigan Warriors: Escare; Davies, Gelling, Isa, Marshall; Williams, Leuluai; Nuuausala, Powell, Flower, Tomkins, Wells, O'Loughlin.
Replacements: Clubb, Tautai, Navarette, Forsyth.
Huddersfield Giants: McIntosh; McGillvary, Cudjoe, Mellor, Murphy; Brough, Gaskell; Rapira, Leeming, Ikahihifo, Roberts, Ta'ai, Clough.
Replacements: Smith, Dickinson, Hinchcliffe, Wakeman.
Wigan went top of Super League despite being held to a draw by Huddersfield Giants at the DW Stadium.