The Giants raced into an 18-point lead inside the opening 15 minutes through Halsall's double and Fenton Rogers before further tries from Wrench, Sam Hewitt and Zane Dunford put them 36-0 up at half-time.
Catalans rallied in the second half despite the dismissal of loose forward Franck Maria for a high tackle, with Ben Condon scoring twice and further efforts from Leo Darrelatour and Charlie Staines, while Wrench also added his second as Giants claimed the spoils.
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Halsall raced 80 metres for an early interception try and prop Rogers barged over for Giants' second before Halsall dived over in the corner to put the home side in control.
Centre Wrench followed up winger Lewis Jagger's break to go over, Hewitt dotted down Tuimoala Lolohea's kick and Dunford crashed over for the Giants' sixth first-half try, with George Flanagan nailing all six conversions.
Catalans responded early in the second half when second row Condon burst over for Toby Sexton to convert, but another converted long-range interception try by Wrench restored Huddersfield's 36-point lead.
Maria was then sent off for the visitors in the 62nd minute for a high tackle on George King and although Catalans went over through Condon's try and efforts from Darrelatour and Staines, they were only consolations.
The Giants remain bottom of the table, but their third straight Super League win came after a club announcement at half-time in which they outlined plans to groundshare with Dewsbury at Flair Stadium next season.
