The Portuguese winger was on target for the Sky Blues opening goal, assisted by Beavon, while Jones was the provider for the home side’s second.
The win earned City a place in the hat for the Quarter-Final draw, which will take place on Thursday morning at 11.30am.
Beavon said: “It was tougher than it might have looked. Playing a young team who were full of energy, but we had a game plan before we set out and it paid off tonight.
“The boy heads were on the game, that is the main thing. Jodi did well for the first goal, cut inside and played the ball in to me and I cut it back for Ruben. Very good goal.
“If Ruben and Jodi are on their game you can’t get near them, causing Brighton all sorts of problems.”
The 32-year old had a hand in two goals on the night, and gave a mature performance as stand-in captain in the absence of conventional skipper Jordan Willis.
City are now three games unbeaten under the management of Russell Slade, with a trip to Chesterfield on the weekend's agenda.
Beavon continued: “It will lift confidence, the last two games we’ve conceded in the last kick of the game so to go out tonight and get three goals and a win was pleasing.
“Wembley would be nice, it is the carrot at the end of it. Which would be a great day out.
“I enjoyed the captaincy, one of the first times I’ve been asked actually.
“I thought we were very comfortable at the back, we played and put it in behind when needed. It is massive on Saturday, we’ll get back on the training field and get ready for it.”