The 22-year-old opened the scoring after the break to set The City Club on the way to their 12th win of the season.
It is his ninth goal in 31 games involving 27 starts in the topflight.
After a barren first half, Dwamena broke the deadlock on 49 minutes when he latched onto Pa Madou Jagne's ball, rounded goalkeeper Tomas Vaclik before slotting the ball into the net.
Jagne then turned finisher in the 62nd minute to put Zurich 2-0 up, before Michael Frey added the third on 82 minutes.
Antonio Marchesano then made it 4-0 in the first minute of injury time before Albian Ajeti pulled one back for the visitors two minutes later.
The result puts Zurich fourth on the league table, two places below Basel.
Dwamena, who joined The City Club from Austria Lustenau in 2017, scored a combined 30 goals over the course of last season.
He was once on the books of Austrian giants Red Bull Salzburg, featuring for feeder side Liefering.
Last summer, he came close to sealing a move to English Premier League new entrants Brighton and Hove Albion.
However, after Zurich and Brighton announced reaching agreement for the transfer of the target man, the move fell through at the eleventh hour as the English outfit reportedly pulled out of the deal over the striker’s failed medical due to a heart condition.