The winger, a 72nd minute substitute, made the most of his limited opportunity with a goal that sealed a 3-0 win at Kilmac Stadium at Dens Park.
It was his third game for Hibs, all three appearances coming as substituted outings.
After a barren first half, Florian Kamberi broke the deadlock with a strike in the 51st minute after being set up by Stephen Mallan.
Nigeria defender Efe Ambrose then assisted Martin Boyle for the second goal, before Agyepong wrapped things up on 88 minutes.
Hibs sit second on the league table after the matchday six win, with Dundee languishing at the bottom-most position.
Agyepong, who joined Hibs on a season-long loan from Manchester City in the summer, would be hoping for better fortunes this time after injury marred his loan stint with Dutch club NAC Breda last term.
Long spells in the treatment room restricted the 21-year-old to just 12 Eredivisie outings involving four starts for NAC in 2017-18, having played 27 times to help the side secure topflight promotion the season before.
In 2015-16, he was on the books of FC Twente.
Agyepong's injury predicaments have put him away from Ghana's national team after a run of games in 2017 following his debut in June.