Fly-half James Arlidge scored a try, a penalty and two conversions as the Dragon cruised past Connacht 23-10 at Rodney Parade in the Magners League on Saturday.
Fly-half Miah Nikora scored all the visitors' points by converting his own try and adding a penalty.
Despite driving rain and a strong wind, the home side made a determined start to force a penalty from which James Arlidge kicked them into the lead.
Dragons did all the early attacking and the opposition back row of Mike McCarthy, Johnny O'Connor and skipper John Muldoon had to make a concerted effort to prevent further scores.
But they were at fault when allowing Danny Lee to break from a scrummage to feed Arlidge, who scored the try and converted it himself.
Conor O'Loughlin made a couple of strong runs for the visitors and some strong forward pressure gave them field position from where O'Connor raced over, only to be recalled by referee Peter Fitzgibbon for a previous infringement.
Some scrambling play on the Dragons' line led to the referee calling on the TV match official for a touchdown decision, which went against the visitors.
But Connacht were not to be denied and Nikora sliced through for a try under the posts that he converted himself.
Arlidge and Nikora exchanged penalties just before half-time to give Dragons an interval lead of 13-10 that was deserved on the balance of play.
With the wind at their backs for the second half, Connacht started to make use of the elements and Nikora was just wide with a dropped goal attempt.
The slippery conditions made handling more difficult and scoring chances were missed on both sides.
Replacement Shaun Connor drove over a penalty to make it 16-10 and in a grandstand finish, Joe Bearman raced 30 metres down the touchline to score with Connor converting.
Tries: Arlidge, Bearman,
Pens:Arlidge 2, Connor
Dragons: 15 Martyn Thomas, 14 Aled Brew, 13 Tom Riley, 12 Rhodri Gomer Davies, 11 Richard Fussell, 10 James Arlidge, 9 Danny Lee, 8 Joe Bearman, 7 James Harris, 6 Dan Lydiate, 5 Luke Charteris (c), 4 Adam Jones, 3 Gethin Robinson, 2 Steve Jones, 1 Hugh Gustafson.
Replacements: 16 Duane Goodfield, 17 Nigel Hall, 18 Hoani MacDonald, 19 Lewis Evans, 20 Will Harries, 21 Shaun Connor, 22 Wayne Evans
Connacht: 15 Gavin Duffy, 14 Liam Bibo, 13 Niva Ta'auso, 12 Keith Matthews, 11 Troy Nathan, 10 Miah Nikora, 9 Conor O'Loughlin, 8 John Muldoon (captain), 7 Johnny O'Connor, 6 Mike McCarthy, 5 Bernie Upton, 4 Michael Swift, 3 Jamie Hagan, 2 Sean Cronin, 1 Ronan Loughney.
Replacements: 16 Adrian Flavin, 17 Brett Wilkinson, 18 Andrew Browne, 19 Mike McComish, 20 Frank Murphy, 21 Ian Keatley, 22 Aidan Wynne.