The visitors were made to work had for their victory, which keeps them in top spot, with an encounter against a plucky Red Devils side.
The Red Devils tied things up in the 13th minute thanks to a Gareth Ellis error.
The Black and Whites skipper forced a pass, Michael Dobson kicked it forward and won the race for the ball to score.
Mistakes crept into both side’s play and the score remained 6-12 until half-time.
Salford cut the deficit to just two points in the 52nd minute.
Dobson found Gareth O’Brien on the right wing who set up Caton-Brown for the try.
O’Brien couldn’t convert so Hull FC had a slender 10-12 lead.
But some magic from sub Chris Green gave the Airlie Birds some breathing space.
He took the ball close to the line, stepped and then fended off a defender for a great try.
Hull FC were in front 10-18 with 19 minutes left on the clock.
Then Lui produced his own piece of individual brilliance, a grubber and regather to score, which put the home side in front 20-18 with 12 minutes to go.
This kicked Hull FC back into gear and Sneyd set up and scored an excellent solo try.
The Airlie Birds had time for another – Ellis setting up Mahe Fonua with an audicious flick pass and the burly centre did the rest through pure power.
Salford hearts were broken as Hull FC finished strongly with two tries in the final nine minutes wrapping up the win.