But they put their RaboDirect PRO12 blues behind them as Wales international winger Aled Brew scored the first try in the five-try win.
Second row Rob Sidoli added a second try before the quarter hour but the Dragons only led 14-3 at half-time.
However Edwards managed to inspire his troops in the second half and South African winger Tonderai Chavhanga continued his impressive start to life in Newport with a first try in European competition just seven minutes into the half.
Since his arrival from the Lions, the 27-year-old flier has made a prolific start to his career with two tries in three RaboDirect PRO12 encounters.
Scrum-half Wayne Evans added the bonus-point try on the hour before Gavin Thomas, who welcomed back Welsh international backrow colleagues Toby Faletau and Dan Lydiate, scored the fifth 15 minutes from time.
The Dragons now turn their attention to next week's clash against Exeter at Rodney Parade as the Chiefs look to bounce back from a 15-12 defeat to Perpignan, orchestrated by former Ospreys' fly-half James Hook.
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