The Pharaohs had to wait until the 66th minute to break the deadlock at the Military Academy stadium, before scoring twice more to beat their east African opponents.
The Rwanda clash came less than two weeks of Egypt's FIFA Confederations Cup, and the former Ghazl Mahalla stars says the pact schedule is taking its toll on the players.
"We have had a schedule packed with very important games over the last 13 months," Gharib said after the game.
"The players have also put so much effort in the Confederations Cup so it's normal if fatigue affected their display tonight."
Gharib added that his players had to cope with enormous pressure prior to and during the game.
"Rwanda drew 0-0 with Algeria and narrowly lost 1-0 to Algeria, so we can be happy with beating them by three goals," Gharib continued.
After drawing with Zambia and losing to Algeria, Egypt had to beat Rwanda and win their next three games to ensure their qualifying group's leadership.
The six-time African champion are now second in Group C with 4 points, more on goal difference than third-placed Zambia.