Ayew, son of the African legend ‘Pele’ Ayew and the BBC Africa Footballer of the Year, and Gyan earned the 2010 World Cup quarter-finalists a 2-0 win over Mali to leave them heading Group D on six points.
But the group will go down to the wire as any one of their three rivals, Guinea, Mali or even pointless Botswana, could still theoretically bag a last eight place.
The final throw of the dice for the Group D inmates comes on Wednesday with Ghana requiring just a draw from their encounter with Guinea in Franceville, with Mali heading off to the Gabonese capital Libreville to face Botswana.
Gyan, who faced a race against injury to be fit, got Ghana off the mark in the 63rd minute when he curled a free-kick past goalkeeper Soumbeyla Diakite.
Then he was instrumental in the second when his back-heel in the 76th minute set up Ayew who skilfully wrongfooted the Mali defence to unleash an unstoppable pile driver past Soumaila Diakite in the Mali goal.
“We had a few difficulties in the first half, but the boys showed strong character and we changed tactics and put pressure on them to make mistakes in the second half,” said Gyan.
The UAE-attached striker added: “This was a very important victory and we hope to continue to make Ghana proud.”
Mali skipper Cedric Kante said they have not given up hope of reaching the quarter-finals.
“We still have our destiny in our hands as it is now down to our last game against Botswana,” said the Greece-based centre half.
“We did not fight, we were not daring and we did not ask questions of the other team.”
Ghana’s win followed a record equalling performance by Guinea, who routed Botswana 6-1 in the first leg of the Group D double bill in Franceville.
Freescoring Guinea matched the record victory margin for a Nations Cup game and they are only the third team after Egypt in 1963 and Ivory Coast in 1970 to have scored six goals in a tournament match.
Goals from Sadio Diallo, who got a double, Abdoul Camara, Ibrahima Traore, Mamadou Bah and Naby Soumah earned Guinea the lopsided win against a side that had been reduced to 10-men when Patrick Motsepe was red carded in first half stoppage time.
Guinea defender Bobo Balde said: “We won 6-1 but football is never easy. No matter how many you goals score, you only get three points.”
Guinea coach Michel Dussuyer said it was crucial they won so as to get their campaign back on course.
“We needed to win because we don’t want to go back home. We were not lucky against Mali, but we were very satisfied we scored many goals in this game,” said the Frenchman.
“Botswana showed in their qualifiers they are a good team and so to score six goals against them was very satisfying for my team.”
Botswana coach Stanley Tshosane commented: “We must accept that Guinea were the better team, even though, three or four of the goals we let in were our own mistakes.
“We are sorry to our fans because we expected what our country expected.
“The better team won, we have been taught a football lesson and we have learnt.”
Monday’s programme moves across the border to Equatorial Guinea where the already qualified Cup co-hosts take on Zambia in Malabo and Libya face down and out Senegal in Bata.