Although handed a limited game time, the striker wasted no time in making his presence felt as The Frogs registered a 3-0 away triumph at Benito Villamarin.
The game was his first competitive outing since making a switch from Swiss side FC Zurich earlier this month.
Dwamena was introduced into Friday's game on the 90th minute mark, replacing Jason, who set up Roger for the opening goal seven minutes to half-time.
Captain Jose Luis Morales made it 2-0 in the 54th minute with a sublime solo effort, before being set up again for the third by Dwamena in stoppage time.
The Ghanaian, who was picked out on a counter break on the left, delivered a low grounder of a cross into the box for Morales to simply tap home from close range in the fifth minute of injury time.
It was a limited but refreshing first bout of action for Dwamena, who would be hoping for more game time when Levante host Celta de Vigo in their second game on August 27.
He joined the Spanish side on a four year deal, having netted 21 league goals in two seasons for Zurich.
Last summer, he came close to joining English Premier League club Brighton and Hove Albion but the move fell through at the last hour due to a failed medical.
Compatriot and club mate Emmanuel Boateng, meanwhile, missed Friday's game due to injury.