The hosts won the game 38-25, scoring four tries in the process.
However, it was the Dragons who started the encounter the better of the two teams, outside centre Adam Hughes scoring with a try.
That lead lasted for just three minutes, though, as Jack Wallace went over for the Wasps.
Wasps went into the break with a 25-15 lead and scored two more tries through Joe Simpson after the interval.
Fly-half Nicky Robinson converted three of his side's tries and kicked four penalties in the match, as Wasps bagged a comfortable win on Saturday.