كتب : وكالات
In-form Cameroonian striker Edet Otobong, who has notched eight league goals so far this season, opened the scoring as early as the eighth minute.
Midfielder Karim Fathallah doubled Ittihad's lead five minutes later and Hussein Fahmi put the result beyond doubt on 22 minutes.
Matrouh's sole goal came in the 32nd minute through a penalty from Mohamed Hosni.
The win will boost the morale of an ailing Ittihad side, who made a disastrous start to their Egyptian Premier League campaign.
They failed to win any game at their stadium in Alexandria, collecting 10 points from 14 games to slip to the bottom of the table.
"This win is a step on the right track," Ittihad coach Mohamed Amer, who succeeded Carlos Cabral after the Brazilian boss was dismissed, said after the match.
"I hope that our first win in Alexandria will end the bad luck we had during the past period."