"We still have 90 more minutes to determine whether we play in Brazil or not," Ghana midfielder Andre Ayew said. "What we have achieved with this scoreline is to have one foot in Brazil. We need to complete it in the next match when we play in Egypt."
After struggling badly at the start, Egypt responded through a 41st-minute penalty by Mohamed Aboutrika to narrow the margin to 2-1, only for an unrelenting Ghana to respond with four more goals.
Majeed Waris put the home team two goals clear again just before halftime, and Gyan scored his second soon after the break. Sulley Muntari added a penalty in the 72nd and a last-minute strike by substitute Christian Atsu ensured Ghana will take a seemingly insurmountable lead into the second leg on Nov. 19.
Ghana coach Kwesi Appiah said simply: "We played well."
Gyan scored with a right-footed shot inside five minutes for the early lead and Egypt goalkeeper Sheri Ekramy had to make sharp saves to deny the Ghanaians another two goals in the first 20 minutes. Ekramy was helpless when Gomaa deflected Michael Essien's shot into the net in the 22nd.
Mohamed Salah was fouled to set up Aboutrika's penalty just before halftime, only for Waris' header to make it 3-1 three minutes later.
Gyan struck for his second with another header in the 53rd, Muntari scored the fifth from the spot after Waris was fouled with 20 minutes to go and Atsu's powerful shot with a minute left capped a surprisingly one-sided game after Egypt was the only team to win all six of its group matches in Africa's qualifying competition.
Ivory Coast and Nigeria won their first legs this weekend, Cameroon drew 0-0 in Tunisia and Algeria had a narrow 3-2 defeat in Burkina Faso. Should Ghana, Ivory Coast, Nigeria, Cameroon and Algeria qualify, as appears likely, Brazil will host the same five African countries that made the last World Cup.