The Welsh side had the boot of Dorian Jones and Carl Meyer to thank as they opened up a second-half lead.
But Stevie McColl's try added to Ben Morgan's first-half effort and it looked like defending champions Gloucester had done enough at Kingsholm.
And Jones - a former Gloucester player - was delighted with the response and the decisive late score from Davies that gave the Dragons only their second victory on the road in 2016.
"I never thought I would be cheered in the Shed again to be honest but the travelling Dragons fans have been great," he said.
"It has been a tough couple of weeks with some tight scorelines but today we came out on top.
"Full credit to the maturity and leadership shown by the squad - the way we managed the game was very special."
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