A first-half red card for Dragons lock Rynard Landman handed Connacht the initiative as they went on to win 30-25 at Rodney Parade on Sunday.
Landman was sent-off for elbowing Jack Carty with the Irish province 10-3 ahead through Craig Ronaldson's try and five points from Carty.
Eoghan Masterson added a second touchdown following the lock's dismissal before the Welsh region reduced the deficit through Hallam Amos' effort and Tom Prydie's second three-pointer.
But two Darragh Leader penalties and a try by Mick Kearney after the break secured the visitors a deserved win, despite Jack Dixon and Amos going over for the Dragons.
After the Dragons' remarkable victory over Leinster last week – their first in Dublin – the Rodney Parade-based outfit were looking to back-up that result.
They duly started the game full of confidence and intent and Prydie's penalty put them into a 3-0 lead. However, Pat Lam's men are a team that have surpassed expectations in 2014/15 and a well-worked move ended in Ronaldson crossing the whitewash.
Carty then kicked a three-pointer to extend the visitors' advantage to seven points before the game's most pivotal moment came when Landman was rightly sent-off for an elbow on the Connacht fly-half. Down to 14 men, the Dragons initially struggled to cope and that was demonstrated through Masterson's close range score.
To the hosts' credit, they displayed plenty of spirit and Amos' try, after Dorian Jones' intelligent pass, got them back into the contest.
Prydie's penalty, the final act of the first-half, reduced the deficit further at the interval, but two Leader efforts off the tee early in the second period kept Lyn Jones' side at arm's length.
The Dragons continued to string phases of play together in incredibly difficult conditions – the constant rain making it a struggle to produce cohesive attacks – and they got their rewards through Dixon's touchdown.
With just five points separating the teams, the Welsh region had a chance to claim a superb victory, but that was extinguished through Kearney's try. However, they managed to rescue a losing bonus-point in the last play of the encounter via Amos' weaving run.
Tries: Amos 2, Dixon
Con: Prydie 2
Pen: Prydie 2
Red card: Landman (use of elbow – 14 mins)
Tries: Ronaldson, Masterson, Kearney
Con: Carty 2, Leader
Pen: Carty, Leader 2
Dragons: 15 Jason Tovey, 14 Tom Prydie, 13 Pat Leach, 12 Jack Dixon, 11 Hallam Amos, 10 Dorian Jones, 9 Jonathan Evans, 8 Nick Crosswell, 7 Nic Cudd, 6 James Thomas, 5 Rynard Landman (c), 4 Andrew Coombs, 3 Brok Harris, 2 T. Rhys Thomas, 1 Boris Stankovich.
Replacements: 16 Rhys Buckley, 17 Phil Price, 18 Dan Way, 19 Ian Gough, 20 James Benjamin, 21 Richie Rees, 22 Ashley Smith, 23 Matthew Pewtner.
Connacht: 15 Darragh Leader, 14 Danie Poolman, 13 Dave McSharry, 12 Craig Ronaldson, 11 Matt Healy, 10 Jack Carty, 9 John Cooney, 8 Eoghan Masterson, 7 Jake Heenan, 6 John Muldoon (c), 5 Aly Muldowney, 4 Quinn Roux, 3 Nathan White, 2 Tom McCartney, 1 Denis Buckley.
Replacements: 16 Shane Delahunt, 17 Rodney Ah You, 18 Finlay Bealham, 19 Mick Kearney, 20 George Naoupu, 21 Ian Porter, 22 Niyi Adeolokun, 23 Tiernan O'Halloran.
Referee: Lloyd Linton (Scotland)
Assistant Referees: Rhys Thomas (Wales), Sean Brickell (Wales)
TMO: Gareth Simmonds (Wales)