Fetu'u Vainikolo scored two tries to help Connacht to a 27-19 win over the Dragons in the Pro12 at Rodney Parade on Friday.
Fly-half Miah Nikora also contributed 17 points as the Irish province recoded just their fifth victory of this RaboDirect Pro12 season.
The Dragons' scores came through a converted Toby Faletau try and four Lewis Robling penalties, but they undid their good work from last week.
The hosts enjoyed a morale-boosting 29-15 victory over Edinburgh then and set their stall out early here when Robling kicked an early penalty.
However, Connacht, who suffered a galling 20-16 defeat at the hands of second-placed Munster in the previous round, responded in excellent fashion.
Former Highlanders wing Vainikolo went over and Nikora converted as the visitors took a 7-3 lead.
The hosts hit back through a penalty from their fly-half, but the away side's pivot converted three opportunities in succession as they opened up a 10-point advantage.
Dan Lydiate was then sin-binned for Newport and Nikora kicked the resultant penalty. Robling added another three-pointer to reduce the deficit, but it was Connacht who were in control at the interval.
And they emphasised their dominance when Vainikolo scampered clear for his second try. Nikora missed the conversion before Robling added his fourth penalty for the Dragons.
However, the visiting fly-half continued his fine form with the boot as he restored their 15-point advantage.
Faletau barged over the whitewash to give the hosts hope, Joe Bedford converting, but it proved to be mere consolation despite Eoghan Grace's late yellow card for Connacht.
Con: S. Jones
Pens: Robling 4
Tries: Vainikolo 2
Pens: Nikora 5
Yellow cards: Lydiate (Dragons - 33rd min); Loughney (Connacht 60th min); Grace (Connacht 76th min)
Dragons: 15 Will Harries, 14 Tonderai Chavanga, 13 Andy Tuilagi, 12 Ashley Smith, 11 Aled Brew, 10 Lewis Robling, 9 Wayne Evans, 8 Toby Faletau, 7 Jevon Groves, 6 Dan Lydiate, 5 Rob Sidoli, 4 Luke Charteris (capt), 3 Nathan Buck, 2 Steve Jones, 1 Phil Price.
Replacements: 16 Sam Parry, 17 Nathan Williams, 18 Dan Way, 19 Lewis Evans, 20 Tom Brown, 21 Joe Bedford, 22 Adam Hughes, 23 Steffan Jones.
Connacht: 15 Gavin Duffy, 14 Fetu'u Vainikolo, 13 Kyle Tonetti, 12 Henry Fa'afili, 11 Tiernan O'Halloran, 10 Miah Nikora, 9 Frank Murphy, 8 John Muldoon, 7 Ray Ofisa, 6 Mick Kearney, 5 Mike McCarthy, 4 Michael Swift, 3 Ronan Loughney, 2 Ethienne Reynecke, 1 Brett Wilkinson.
Replacements: 16 Adrian Flavin, 17 Finlay Bealham, 18 Rodney Ah You, 19 Eoin McKeon, 20 Eoghan Grace, 21 Paul O'Donohoe, 22 Matthew Jarvis, 23 Dave McSharry.
Venue: Rodney Parade
Referee: Giuseppe Vivarini (Italy)
Assistant referees: James Jones (Wales), David Jones (Wales)
Television match official: Neil Ballard (Wales)