The Eagles scored three touchdowns for a 19-0 lead in the first quarter with Josh Singleton completing passes of 38, 37 and 53 yards.
Lloyd Grogan caught the first scoring pass for 38 yards and Luke Landry snagged the second for 37 yards.
Grogan capped off the early outburst on a 53-yard catch.
Trevor Derouen put Gueydan on the scoreboard early in the second quarter with a one-yard run, but it was the only point the Bears could muster.
Singleton scored on a 48 yard run in the second quarter for a 26-7 lead.
Dontrell Brown got in on the scoring with a 20-yard catch from Singleton for a touchdown. Jovan Johnson added a 35-yard scoring run in the third quarter for a 39-7 lead heading into the fourth quarter.
Brent Green add a 13-yard scoring run and Eriq Blanchard scored the longest touchdown of the game to cap off the district win on a 57-yard run.
Central Catholic improves to 7-1 overall and 2-0 in District 8-1A with the win. Next up for the Eagles is a trip to face rival Hanson Memorial on Friday.