Leading 14-6 at the start of the second half, Zac Woolford broke from dummy half and found Evalds to score Huddersfield’s third try.
Needing a response, Leigh released Josh Charnley up the right wing and sent Hanley over on his 100th Super League appearance.
But Huddersfield forced a goal-line drop-out that was taken short, Giants claimed the kick and they drove towards the line before Woolford grubbered in-goal for Geyer to dot down.
Leigh kept themselves alive again as they reclaimed the restart, were immediately in behind the defence and sent Mulhern over from the next play.
But they soon knocked on to give Huddersfield field position and Geyer found a gap to slide in for his second try to seal the game.
Huddersfield: Evalds; Milne, Jagger, Halsall, Zenon; Lolohea, Clune; Powell, Woolford, King, Hewitt, Cozza, Rushton
Interchanges: Rogers, Flanagan, Billington, Geyer
Leigh: O’Brien; Senior, Badrock, Hanley, Charnley; Cook, Lam; Ofahengaue, Horne, Mulhern, Hughes, Trout, Liu
Interchanges: Brogan, Ashworth, Alick-Wiencke, Ipape
Referee: Tara Jones
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