Winger Jermaine McGillvary scored twice and was among seven different try-scorers as Paul Anderson’s side - joint-bottom of Super League beforehand - produced the sort of rampant display they have long threatened.
Cudjoe did not cross himself but it was the England centre’s finery that stood out as his line-breaks and deft hands caused havoc for hapless Saints.
Huddersfield, with only their fourth win of the year, were 34-6 up after Aaron Murphy’s remarkable effort in the 54 minute and could really have racked up a bigger scoreline.
Anderson, though, had few complaints and admitted: “That’s been building for a good month or so now.
“Even though we lost last week we were pretty good in France with such a young team and had Catalans on the ropes.
“Today we showed real patience against a Saints side that were just a couple of points off top.
“But we probably had our most experienced side all year and it showed, when we’ve got that and blended with some good youth, we’re hard to handle.”
Huddersfield gave a debut to second-row Sebastine Ikahihifo, their signing from St George Illawarra, and also saw Scott Grix make his first appearance since injuring his shoulder in the opening day defeat at Saints.
It is a sign of Anderson’s faith in the veteran full-back that he came straight back in at the expense of Ryan Brierley, the prolific capture from Leigh Centurions.
“It absolutely was a big call,” he said. “Ryan’s going to be a very, very good player for this cub for a long, long time.
“But he’s still learning the full-back role and I just felt we were going to need a bit more stability in defence so we went back to Grixy’s experience.
“Saints asked a lot of questions of us early on but I was really happy with our resolve on the big stage and in a big game.”
There was no score in the opening quarter but then three tries in just seven minutes from Giants put them in control
Huddersfield did plenty of defending in the first half but were more than up to the challenge.
Indeed, before opening the scoring in the 21st minute, they had created the better chances with Cudjoe and McGillvary both raiding well down the right.
It was Cudjoe, the England centre currently in fine form, who created that first try, stepping out of a tackle on halfway for Joe Wardle and Jamie Ellis to send Grix racing for the posts.
The full-back was hauled down by Shannon McDonnell but, at the next play, sharp hands again saw Cudjoe feed McGillvary.
Danny Brough slotted the first of his eight goals, adding his second when young Saints debutant Calvin Wellington spilled 10m from his own line to gift Ukuma Ta’ai an easy score.
Ruthless Giants then raced away in the next set, too, smart handling down the left seeing Murphy advance from his own half, Jamie Ellis supporting on his inside to celebrate a new three-year deal by sprinting in from 30m.
Beleaguered Saints looked bereft of confidence but finally managed to reply via ex-Giant Matty Dawson in the 35th minute.
Luke Walsh’s kick saw them trail 16-6 at the break but Anderson’s side were over within 65 seconds of the restart courtesy of McGillvary’s second.
It was a sublime effort involving countless offloads before Cudjoe again supplied the final pass although, admittedly, referee Ben Thaler did miss a blatant forward pass from Brough at the start of the thrilling move.
There was no debating Sam Rapira try in the 50th minute, though, as he bundled over from close range from Kyle Wood’s short pass and then Murphy claimed a bizarre score his own.
Brough’s wayward pass was kicked up in the air by Connor who then had to look around to see where the ball was.
When he found it, the centre leapt to collect and handed onto his winger in one motion for a surreal effort.
Brough’s conversion made it 34-6 but Anderson’s side then dozed to allow Jack Owens a try and, when Grix dropped a high kick, Theo Fages.
Brough’s penalty settled them but Swift crossed in the corner and it needed Ryan Hinchcliffe to restore some order by dummying over for his first Giants try since joining from Melbourne Storm last winter.
Cudjoe, fittingly, eased clear one last time to put Wood over at the death.
St Helens: McDonnell; Owens, Wellington, Dawson, Swift; Fages, Walsh; Tasi, Roby, Amor, Wilkin, Vea, McCarthy-Scarsbrook. Substitutes: Turner, Walmsley, Savelio, Knowles.
Huddersfield Giants: Grix; McGillvary, Cudjoe, Connor, Murphy; Brought, ellis; Crabtree, Hinchcliffe, Mason, Wardle, Ta’ai, Lawrence. Substitutes: Wood, Rapira, Ikahihifo.
Referee: Ben Thaler (Wakefield)