Hudson thundered home when the ball fell to him in the penalty area to give Cardiff, playing in their new red strip for the first time in a competitive fixture, the three points on a night that had looked set to end in frustration.
The result was harsh on the Terriers, who looked assured on their return to the npower Championship, with the impressive Oliver Norwood and Scott Arfield forcing excellent saves from Cardiff keeper David Marshall, but it was not enough.
Cardiff manager Malky Mackay made 10 changes to the side beaten by Northampton in the Capital One Cup, with Heidar Helguson the only survivor.
Huddersfield had Lee Novak up front while Jordan Rhodes, who has been linked with a move to Blackburn, was not in the squad following his midweek outing for Scotland.
After the furore over the switch from blue to red, Cardiff received a rapturous reception but it was the visitors who settled better.
They crafted an early opening down the right for Arfield from Novak's pass, but Marshall made a sharp, low save to deny him.
The Scotland international was called into action again after 12 minutes as Norwood was given far too much time to line up a strike from distance, Marshall parrying his fierce drive.
Cardiff barely threatened until Jordon Mutch had a half-chance after 20 minutes.
Helguson's intelligent knockdown gave the summer signing room to get away a strike on the edge of the area, but he could not keep his shot down.
Norwood almost gave the Terriers the lead six minutes before the break but his wonderful dipping volley was tipped away by an agile save from Marshall as the opening half ended with a burst of activity.
Helguson hit the bar after Ben Turner headed a Bellamy corner back across goal, while the lively Norwood could not control Sean Scannell's cross after the midfielder had rounded Marshall.
Cardiff were struggling to get Bellamy and Peter Whittingham into the game as they opted to pump the ball long to Helguson, which the Huddersfield back four dealt with comfortably.
The Terriers continued to carve out the clearer of the openings with Jack Hunt's driving run to the edge of the box ending with the full-back fizzing a strike inches over the bar.
The hosts then spurned a great opportunity on 64 minutes. Alex Smithies failed to hold Mutch's angled drive and Helguson looked certain to tap in, only for the covering Peter Clarke to brilliantly deny the forward.
It was Smithies' turn to help out Clarke seven minutes later after Bellamy had tricked his way past the centre-half, the keeper making a sprawling stop to deny Kevin McNaughton from the Wales international's pull-back.
Marshall pushed an Arfield effort around the post from Keith Southern's pass while substitute Joe Mason blazed over for the hosts with what appeared to be their last chance, until Hudson came to the rescue.