The West Yorkshire club - tipped for big things after Watson's arrival from Salford Red Devils - were competitive throughout at St Helens but gave away far too many penalties and were too lax in possession at times.
Nevertheless, they were still chasing hard trailing 20-10 when England second-row Greenwood was dismissed for a swinging arm on Samisoni Langi in the 76th minute, summing up their afternoon.
Catalans - who backed up their opening round win against Hull KR - also boasted the game’s best player in Sam Tomkins, the England full-back who played a decisive role in two of their tries.
Just as they were for the loss against Hull FC on Sunday, Huddersfield were once more without their ‘marquee’ signing, captain and scrum-half Aidan Sezer who remains sidelined by injury for at least another two weeks.
They needed him back soon to help bring more control although Lee Gaskell, who switched from full-back to half-back in place of Olly Russell, was arguably Giants’ top performer.
Darnell McIntosh moved to No1 with Sam Wood - who scored one of of Huddersfield’s two tries - earning his first appearance of the season on the wing.
Similarly, Jake Wardle came in for Ricky Leutele and club captain Michael Lawrence also returned for his 300th career game.
After Wood’s try, from Gaskell’s lovely floated pass in the 58th minute, Huddersfield threw everything at their French opponents but could not claw the deficit back.
Jack Cogger wasted one chance with an awful forward pass to Lawrence and Tom Davies produced a try-saving tackle to deny Wood a second try before Greenwood’s moment of madness.
Catalans had opened the scoring after just six minutes, Tomkins making a typically mazy run to get close and - though denied by James Gavet - still be able to squeeze out a pass for Matt Whitley.
James Maloney improved and his side immediately heaped more pressure on as they burst through from the restart.
Tomkins’ kick forced a goalline drop-out but Huddersfield were relieved to see Gaskell’s kick bounce in to touch.
Watson’s side actually scored with their first real attack, Gaskell supplying the clever pass for Chris McQueen to get over untouched wide on the right.
Gaskell converted the 12th minute score and a fine McIntosh pass unleashed Jermaine McGillvary soon after.
The England winger seemed destined to score in the corner but Tomkins somehow got across and managed to force the ball clear with the ferocity of his last-ditch tackle.
McGillvary looked groggy afterwards - there was question marks over whether Tomkins had made high contact - but Huddersfield should certainly have added to their score when Maloney was sin-binned for a dangerous challenge in the 23rd minute.
Again, though, they misfired, Greenwood somehow ending up kicking on the last tackle and Watson’s side failed to score against the 12 men.
The busiest man on the Catalans side seemed to be their kit man who had to come on three times in a stop-start first period, firstly to replace Dean Whare’s shirt after the Kiwi centre suffered a bloodied nose and then again to give him some new shorts.
Jason Baitieri also required a jersey change following a head wound yet, remarkably, when Catalans were down to 11 men with him and Maloney off the field, the French side scored.
Garcia claimed Tomkins’ chip to score, Tomkins converting before Maloney returned to add a penalty after yet more ill-discipline.
To rub it in, Tomkins claimed Gaskell’s kick and brilliantly unleashed Tom Davies who sprinted downfield and beat McIntosh.
Wardle just got back to deny him but the Catalans winger found Mike McMeeken as he fell and his side went in 20-6 ahead.
It was a crucial score; both sides were well-matched in the second half as Huddersfield improved and sought to get back into the contest.
However, it is two defeats from two outings for Watson.
Huddersfield Giants: McIntosh; McGillvary, Cudjoe, Jake Wardle, Wood; Gaskell, Cogger; Yates, Cunningham, Gavet, McQueen, Greenwood, Jones. Substitutes: English, Edwards, O’Brien, Lawrence.
Catalans Dragons: S Tomkins; Davies, Langi, Whare, Yaha; Maloney, Drinkwater, Dudson, Da Costa, Bousquetm Whitley, McMeeken, Garcia. Substitutes: Morgue, Seguier, Baitieri, Kasiano.
Referee: Ben Thaler (Wakefield)
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