Salford were in command from the start and built a 20-0 by half-time with converted tries from George Griffin, Caton-Brown and Weller Hauraki, with Gareth O’Brien also booting a penalty.
Ben Murdoch-Masila and Caton-Brown, with a brace, added second-half touchdowns with O’Brien finishing with five kicks from seven attempts as Salford claimed a comfortable victory.
Huddersfield, who have now lost four games in a row, were 24-0 down before they finally got on the scoreboard with substitutes Nathan Mason and Oliver Roberts scoring in quick succession, but they never looked like turning the match around.
A mistake from returning Huddersfield full-back Scott Grix, who fumbled a kick from Mateo, put the Giants under pressure and Salford took advantage with George Griffin ploughing over the line.
Salford were in dominant mood and six minutes later slick passing between Mark Flanagan, Michael Dobson and Josh Griffin put Caton-Brown over in the corner for his opening try of the match.
O’Brien, having converted both those scores, extended the lead to 14-0 with a penalty.
Eorl Crabtree’s introduction off the bench helped Huddersfield build some forward momentum, with Danny Brough’s tactical kicking also pegging the Red Devils back a bit.
However, it was still Salford who looked the more likely scorers and after Caton-Brown had a try ruled out for a forward Dobson sent Hauraki stretching over for his first try of the season and O’Brien again landing the conversion to make it 20-0 at the break.
That left Huddersfield with a mountain to climb but they could have trimmed Salford’s lead early in the second half if Leroy Cudjoe had managed to find Gene Ormsby, but a poor pass saw the opportunity go to waste.
Justin Carney was proving a handful for the Giants on his return to the Salford side and another burst created the platform for Murdoch-Masila to notch the Red Devils’ fourth try.
That stretched the hosts’ lead to 24-0 but Huddersfield finally breached the Red Devils defence when Mason forced his way over.
Soon after Roberts also crossed the line and, with Brough converting both, Huddersfield had a glimmer of hope at 24-12.
But any chance of the Giants making further in-roads were hit as Caton-Brown ran in further tries.
Giants coach Rick Stone said: “It’s tough to take and we were on the back foot from the start and were left chasing our tails.”
Salford: O’Brien, Carney, J. Griffin, Sa’u, Caton-Brown, Lui, Dobson, Kopczak, Tomkins, G. Griffin, Murdoch-Masila, Mateo, Flanagan. Substitutes: Hauraki, Burgess, Krasniqi, Kenny.
Huddersfield: Grix, Ormsby, Cudjoe, Connor, Murphy, Brough, Ellis, Rapira, Hinchcliffe, Huby, Ta’ai, Lawrence, Ikahihifo. Substitutions: K. Wood, Roberts, Crabtree, Mason.
Referee: J Child (RFL).