Thornley found Bevan French on the right-hand touchline and he showed impressive speed to race down the flank and then intelligence to find Field with a perfect inside pass which sent the Australian full-back over the line.
Smith converted to make it 12-10 and put Wigan ahead for the first time.
Lolohea’s misery with the boot continued in the 49th minute when he failed to convert a penalty.
A crossfield kick by Cust then forced McGillvary into a goal-line drop-out, but as the hour mark approached, Wigan forward Smithies conceded a costly penalty.
Smithies, having escaped punishment for an earlier high shot on Joe Greenwood, caught Leutele with a similar challenge.
Referee James Child opted not to sinbin Smithies, much to the anger of the Huddersfield fans, but from the resultant penalty the Giants worked the ball out to the right flank.
Centre Leroy Cudjoe’s delightful offload found team-mate McGillvary and he pounced to score in the corner.
Once again, Lolohea faltered with the boot, leaving him with one goal from five attempts and the scores finely poised at 14-12 in Huddersfield’s favour.
It was an advantage they could not protect as Marshall’s predatory finish from Smith’s sumptuous kick delivered a killer blow.
Huddersfield Giants: Lolohea; McGillvary, Cudjoe, Leutele, Senior; Cogger, Russell; Hill, Levi, Wilson, Jones, McQueen, Yates; Interchange: English, Greenwood, Trout, Golding
Wigan Warriors: Field; French, Thornley, Bibby, Marshall; Cust, Smith; Singleton, O’Neill, Byrne, Farrell, Bateman, Smithies; Interchange: Leuluai, Mago, Ellis, Havard
Referee: James Child