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The Terriers saw their penalty claims turned down early on when Ashley Vincent appeared to handle Peter Clarke's header on the line.
U's goalkeeper Ben Williams then prevented team-mate Magnus Okuonghae from scoring an own goal, before fellow custodian Ian Bennett denied David Perkins at the other end.
Huddersfield took the lead 11 minutes before half-time through Lee Novak, who planted a low decisive shot past Williams from 20 yards after David Mooney had given away possession.
And the Terriers doubled their advantage three minutes prior to the break when Anthony Pilkington clinically finished from Novak's pass.
Colchester started the second half well and Mooney crashed a 30-yard effort against the crossbar.
But substitute Jordan Rhodes sealed Huddersfield's victory with 11 minutes remaining after polishing off Joe Garner's flick-on.
And although another Terriers substitute Lee Croft was dismissed for two bookable offences with 10 minutes to go, it was all academic.