Amr Zaki put Egypt ahead on 27 minutes but Zambia secured a share of spoils through a Francis Kasonde header 12 minutes after the restart.
Substitute Mohamed Abou-Treika had a glorious opportunity to give Egypt all three points late in the game, but his close-range shot was superbly blocked by Mweene.
"Our keeper played a fantastic game," French tactician Renard told the post-match press conference.
"His saves denied Egypt from scoring another goal.
"We had a good start but, unfortunately, slowed down after scoring the opener. Luck was on our side in the second period."
Zambia, who have never played in the World Cup, next face Rwanda at home on the sixth of June.
"Our match against Rwanda will be difficult because they will do their best to qualify for the African Cup of Nations," Renard added.