"We are not the same side that played good stuff last year but we are getting there", said Dragons head coach Paul Turner.
"I'm really pleased with the players after the weekend. You always build yourself up for the weekend and there's no doubt the players were up for it after the loss to Connacht last week."
In a scrappy and often ill-tempered match, the Dragons scored all their points in the first half, going in for the break with a 23-3 lead. In a complete reversal, Glasgow dominated the second half but ultimately came up short.
Jason Tovey opened the scoring for the hosts with an early penalty, only to leave the field seconds later with a hamstring injury. That didn't deter the Men of Gwent, however, with replacement Matthew Jones adding two further penalties before Robin Sowden-Taylor and Aled Brew barged their way over for tries, which Jones duly converted.
Glasgow came out for the second half fired up and soon struck back when Richie Vernon put Richie Gray over to score. Ruaridh Jackson soon added a monstrous penalty to bring the scores to 23-11 but that was all the visitors could manage despite their second-half dominance.
"The guys didn't front up in the first half and the Dragons had a little bit more desire", said Warriors head coach Sean Lineen.
"We got bullied up front, there was no direction, we were too slow to clear the ball, nobody wanted the ball and we waited to see what they had.
"We knew the first 20 was going to be really important, whether playing into the wind affected the side I don't know, but there was just no spark.
"There are no excuses, absolutely none. The lads are better than that. It's part of the learning curve, there were a lot of youngsters out there and we just didn't front up.
"In the second half we got a few guys on and the two Richie's stood up. But any time we got momentum something happened. A lot of guys are disappointed with the overall performance but it was only the second game of the season and a lot of the lads will learn from that."
Both teams will have to endure a tough series of Magners League matches before they meet in Europe's showpiece competition and their respective coaches will be hoping their squads stay injury free while they also expect to see the return of a number of influential players.
With a further three fixtures under their belts, both sides will go into their Pool 6 opener on Sunday, October 3 in better stead having banished any early-season teething problems.