كتب : Omar AbdelAziz
Barakat hit a fine brace after Flavio Amado's opener, while the in-form Ahmed Sedik completed the rout in injury time.
The league holders moved up two spots to lie fourth in the table with 23 points, seven less than leaders Petrojet, but the latter played four more games.
Manuel Jose handed rare starts to Hussein Ali, Ahmed Hassan Farag and Abdul-Hamid Ahmed, who had a nervy full-debut at Cairo stadium.
Key men Gilberto and Mohamed Abou-Treika were left on the bench, while Ahmed Hassan was rested.
Late Action
Ahli seemed to struggle in breaching an ultra-defensive Tersana side early in the game, with some shy attempts on goal by the lively Farag.
The former Ghazl Mahalla hitman looked determinant to prove his worth and created danger in the air, but needed some accuracy to hit the target.
However, Farag's work rate paid off in the 37th minute, when he won a clever freekick at the left flank, even though it was Flavio who collected the benefits.
The Angolan reacted swiftly with Ahmed Fathi's low cross, to poke home his fifth of the season.
Three minutes from half-time, Sedik sent Barakat through on goal, and the latter showed no nerves to slot home between the legs of Joao Raphael.
Same Scenario
Hassan Mostafa made his season debut in the second half, coming in for Ali, as Jose's side almost repeated their late first-half raid on the league strugglers.
The second half barely witnessed any genuine action at both ends, until three minutes from the final whistle.
Center-half Ahmed Al-Sayed made a brave run to break into Tersana's area, before sending a fine cross to Barakat, who jabbed in from close range to hit the net with the help of goalkeeper Raphael.
The match was virtually over, but man of the match Barakat still had more to give before the end.
The versatile midfielder returned the favor to Sedik with a brilliant assist in stoppage time, as the latter notched in the easiest of goals, scoring his second in two games.