The 18-year-old came off the bench in the 75th minute of Roma's game at Genoa, and netted a late double to give the Giallorossi a 2-0 win.
Ghanaian Afena-Gyan ran to the bench to celebrate with his manager after breaking the deadlock when he slotted in a pass from Henrikh Mkhitaryan in the 82nd minute.
"I promised him a very expensive pair of shoes, for 800 euros, and he came to me to make sure I didn't forget," Mourinho told broadcaster DAZN.
"I really like his coldness, his physicality but above all his humility."
Afena-Gyan then added a stunning long-range strike in injury time to wrap up the points at the Stadio Luigi Ferraris and move Roma up to fifth in the table.
Mourinho made good on his promise and presented the youngster with the shoes on Monday.
After the match in Genoa Afena-Gyan spoke of his "great feelings" as he thanked his family for their support.
"I have to say a big thanks to God Almighty for what he has done for me tonight," he told the Roma website.
"I dedicate the goals to the club, to the supporters, to everyone, to my family and to my mum. Mum... thank you so much for how far you have brought me. I really appreciate it."
Teen pays tribute to Mourinho
Afena-Gyan was handed his senior debut by Mourinho from the bench against Cagliari on 27 October, and he also featured as a half-time substitute against AC Milan before the international break.
The teenager's progress is being closely monitored by Ghana's national set-up.
He was called up by the Black Stars for their World Cup qualifiers against Ethiopia and South Africa this month, but turned down the chance to join the squad.
Afena-Gyan paid tribute to the Portuguese, who he describes as a "great person", following his goalscoring exploits.
"He is teaching me a lot and I am learning a lot from him," he added.
"He is someone who has achieved a lot during his career and he is a great person. I am glad to be working with him.
"He encourages me day-in and day-out to do everything that will help me improve in future. So I am happy to be working with Jose Mourinho. I thank him very, very much."
Elsewhere in Italy, Ghana midfielder Alfred Duncan scored the opener as Fiorentina beat AC Milan 4-3, and Nigerian striker David Okereke scored the only goal as Venezia won 1-0 at Bologna.