Egyptian world-known striker Mohamed Salah, now playing for Liverpool, was the man of the match as he scored Egypt's two goals in the 63rd and 93rd minutes of the match.
After Nigeria became the first African country to qualify for Russian Federation 2018 world cup after beating Zambia 1:0 though in a controversial way, Egypt followed suit.
Egypt's President Abdul Fattah al-Sisi has now given a bonus of $85,000 (£65,000) to each of the players who clinched a place at the 2018 World Cup finals in Russian Federation.
A 2-1 win over Congo Brazzaville saw them qualify for the global showpiece for the first time since 1990.
"Maybe we don't play handsome football but we are at the World Cup and that's the most important thing", Cuper said.
He added: "When I stepped up to take the penalty, I didn't think of anything but scoring and winning the game. The most hard moment in my life was when the fans fell silent following Congo's equaliser, but thank God and we finally realised a childhood dream of my own". "I am very happy to lead Egypt to a World Cup after 28 years and to make 100 million [Egyptians] proud of us".
Egypt will now finish top of Group E, making sure of its place at the World Cup with a game to spare against Ghana next month.
"I want to thank the fans, the ones who were in the stadium and everyone in every part of Egypt".
Speaking earlier this year, Sisi blamed the country's woes on Egypt's overpopulation crisis as one of the major challenges confronting the state, saying that the population is now four and a half times what it was in 1952.