Rhodes swept the home side in front with a neat near-post finish in the third minute of Saturday's League One clash at the Galpharm Stadium, only for Kayode Odejayi to level for Colchester two minutes later.
Odejayi out-muscled Town skipper Peter Clarke in the race for Kemal Izzet's through-ball and drilled a shot into the bottom corner from about 12 yards.
Michail Antonio, on loan from Reading, put Colchester 2-1 in front in the 27th minute with a powerful header from Ian Henderson's cross.
But Huddersfield roared back after the break and levelled when Rhodes unleashed a stunning long-range shot into the roof of the net in the 59th minute.
Lee Novak fired his fourth goal of the season in the 64th minute with a delicate lob over Cousins from 20 yards.