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The Dragons surged to a commanding 28-4 halftime lead on Saturday night before the Cowboys scored three straight tries to get within six points with 16 minutes remaining.
However, in front of a healthy 13,886 crowd at WIN Stadium, the home side held on to secure their fifth victory on the trot and hold pole position for the first time in three years.
Centre Tim Lafai bagged a double, while reborn five-eighth Gareth Widdop continued his stellar start to the season by scoring a try and playing a hand in three others.
Their 28 first-half points were the most in 13 years for the Dragons, and the 24-point halftime lead was their biggest in the post-Wayne Bennett era. In the end, it was enough to claim the win.
But for the Cowboys, without five topliners including Johnathan Thurston, their second straight defeat means they are likely to fall out of the top eight by the end of the round.
Despite Cowboys winger Gideon Gela-Mosby cancelling Nene Macdonald's ninth-minute opener, a rout was on the cards when the Dragons scored four straight tries in the first half.
Lafai was a man possessed on the Dragons' left edge, terrorising opposite centre Justin O'Neill to bag two tries, punctuated by a flick pass for winger Kurt Mann.
Widdop also finished off a Russell Packer break to score his sixth try of the year.
But the Cowboys flipped the script in the second half when Ben Spina and Michael Morgan scored in the space of seven minutes to cut the deficit to 12 points.
The unthinkable was then on the cards when Scott Bolton latched onto a spilt Macdonald bomb in the next set, however the Dragons clung on to continue their strong start to the year.