Gouna, who were on the back foot throughout the match, wasted an opportunity to grab the lead against the run of play when they were awarded a penalty one minute after the restart.
Former Zamalek forward Gamal Hamza, Gouna's most prominent player who terminated his deal with Egyptian champions Ahli few months after joining them in the summer, stepped up but saw his effort strike the post.
Gouna striker Ahmed Hassan Farag had a goal ruled out for offside few minutes later.
Wadi Degla had the better chances though but could not end the resistance of Gouna until the 84th minute when Mostafa Talaat broke the deadlock.
Midfielder Ashour Al-Taqui wrapped up the victory deep in stoppage time after scoring his third goal of the season.
Degla, who are owned by Egyptian businessman Maged Samir, recovered from a poor start to their maiden top-flight campaign to register two successive victories.
They lie tenth in the 16-team league table with nine points from eight games.