The home side wrestled to a 10-8 lead in the second half, before a Justin O'Neill try swung the momentum in the Cowboys' favour.
Warriors coach Stephen Kearney says it was a very similar performance to last week's loss to the Rabbitohs.
The result sees the Warriors slump to a 2-4 record for the season.
The Dragons other winners last night, beating Manly 12-10.