It was one of those ugly wins but head coach Paul Turner saw his side earn a fifth triumph of the campaign which lifts the Welshmen above Glasgow Warriors into ninth spot.
In a first half that had few sparks, the Welsh region led by just a single point as the teams went in at the interval.
One player who must have impressed Gatland was wing Aled Brew, who played in November against Fiji. He scored the first of the Dragons’ two touchdowns in the opening period and set up centre Tom Riley for the second.
Brew went over after just three minutes when outside half Jason Tovey fed former Welsh cap Gavin Thomas. Brew took the ball down the left, linked with Riley on the touchline before taking the return pass inside.
Tovey booted the conversion but the he was guilty of arguably the penalty miss of the season so far when a straight-forward 20-metre effort in front of the posts went wide.
Connacht battled hard and caused some problems in the home defence.
After full-back Ian Keatley had kicked a penalty to get the Irishmen started, he converted a try from wing Troy Nathan, who was put away on the right wing by centre Eoin Griffin to give Connacht the lead.
With five minutes to go, however, full-back Will Harries set Brew on another dash from the halfway line where he passed inside to Riley for a converted score although the pass did look suspiciously forward.
But, when Dragons skipper Tom Willis was offside at a ruck 30 metres from his line, Keatley did the honours with his second penalty.
Keatley regained the lead for Connacht on 51 minutes but when hooker Sean Cronin prevented the ball from being released at a ruck, Tovey landed the penalty from 38 metres.
With time running out, Connacht outside-half Miah Nikora tried a decent drop-goal attempt only for replacement flanker Andrew Coombs to charge it down.
Connacht coach Eric Elwood was bitterly disappointed with the result but was able to find positives in the performance.
Elwood said: “We’re disappointed with the result it was a game that we were targeting especially after beating them at home earlier in the season.
“It was a big game for both sides and me made far too many errors and we did not do enough.
Newport-Gwent D’gons scorers: Tries: A. Brew, Riley. Cons: Tovey 2. Pens: Tovey.
NEWPORT-GWENT D’GONS: Harries, Hughes, Riley, Smith, A. Brew, Tovey, J. Evans, Gustafson, Willis, Castle, A. Jones, Sidoli, L. Evans, G. Thomas, Faletau.
Replacements: Price for Gustafson (53), S. Jones for Willis (65), Charteris for A. Jones (56), Coombs for L. Evans (71).
Connacht scorers: Tries: Nathan. Cons: Keatley. Pens: Keatley 3.
CONNACHT: Keatley, Nathan, Griffin, Matthews, Carr, Nikora, Willis, Wilkinson, Cronin, Hagan, Swift, McCarthy, A. Browne, O’Connor, McKeown.
Replacements: Ta’auso for Matthews (73), F. Murphy for Willis (47), Flavin for Cronin (66), Ah You for Hagan (69), Upton for McCarthy (79), McComish for McKeown (55).
Referee: Alan Lewis (Ireland).