Ulster ran in four tries to condemn the Dragons to another away defeat who left Belfast with just four Jason Tovey penalties to their name.
Tovey kicked the Welsh side ahead after seven minutes with his first penalty but the hosts responded with two tries in quick succession to take control of the game.
Number 8 Robbie Diack powered over after 13 minutes and he was swiftly followed over the line by South African Ruan Pienaar.
Pienaar rounded off a sweeping move to claim Ulster’s second try and put his earlier misses behind him to slot the conversion.
Tovey reduced the deficit with two quick penalties but Pienaar kicked another three points to take his side into the break 15-9 ahead.
The Dragons fly-half was the first name on the score-sheet in the second period but his early three points were again quickly cancelled out as Craig Gilroy touched down just a minute later.
The Dragons continued to press but another Pienaar penalty followed by a converted Stefan Terblanche try secured the victory for Ulster.
