It was the Dragons who took the lead after 14 minutes when Benjamin Garcia, who was making his second debut for the club following a return from Penrith Panthers, managed to ground a grubber kick from Glenn Stewart.
Pat Richards missed the conversion to make it just a four-point lead.
Hull then went in front seven minutes later after a kick wasn’t dealt with by the Catalans defence and the ball bounced perfectly for Steve Michaels.
The Australian got his first try of this year’s tournament and Marc Sneyd converted to put the Black and Whites into the lead.
Sneyd added the extra two points to give his side an 8-0 advantage.
Hull then scored the first points in the second half, 10 minutes in as Scott Taylor powered his way through the first line of the Dragons defence and passed inside to Houghton for an easy try.
Sneyd kept up his 100% record with the boot to increase his sides lead to 14 points.
Catalans needed to score next and they did through their teenage winger Fouad Yaha after a great move that saw them go from the middle right out to left, leaving Yaha in space to get his second try of the competition.
Richards missed his conversion again, meaning the Dragons deficit had been reduced to 10.
Sneyd then punished Eloi Pelissier, for stopping Taylor from playing the ball, by extending the lead to 22-8.
The score remained the same and the result means Hull FC are into the semi-finals again for the first time since 2013, the year they reached the final.