Maule's try made the win comfortable for the Dragons
Dragons: (11) 23
Tries: Charvis, Maule, Fussell
Con: A Thomas
Pens: A Thomas (2)
Connacht: (0) 0
The Dragons secured a shot at next season's Heineken Cup with a low-key win over a disheartened Connacht team.
Colin Charvis set the home side on their way with a short-range try, Gareth Maule and Richard Fussell crossing after the break.
Aled Thomas added eight points, Connacht not troubling the scorers.
But Charvis, Kevin Morgan and Aled Brew joined the Dragons' injury list, who face an 18 May Heineken Cup play-off against the third-best Italian side.
Overmach Parma beat the Dragons in last year's corresponding fixture, but this season's potential tie will depend on whether a future can be agreed for Europe's premier club tournament.
With the battle-weary Dragons having lost five in a row and Connacht having little to play for, the slow start at Rodney Parade could have been predicted.
Opposing outside-halves Thomas and Paul Warwick missed straightforward kicks, before Thomas got the Dragons going with a 21st-minute penalty.
Brew then went close with a kick and chase, setting the position for a close-range driving maul, Charvis taking control to cross for the opening try.
That was a hell of a performance with so many players out and after so many games in a short space of time.
Dragons coach Paul Turner
The home side saw captain Morgan pull up sharply with an apparent hamstring injury, but Thomas' second penalty stretched their lead to 11-0 at the break.
Wales summer tourist Brew limped off with a knee injury at the start of the second half to increase the Dragons' injury woes.
Wing Conor McPhillips blew a good chance to get Connacht into the match, cutting inside on the Dragons' 22 but failing to gather a simple pass.
Dragons opposite number Fussell then tore the visitors' defence apart, pouncing on a beautifully weighted Thomas pass in midfield.
Fussell was hauled down inches short, but Gareth Maule was in close support and dived over for the second try.
Connacht's frustration was compounded as flanker John Muldoon was yellow-carded for dangerous driving play at a ruck.
The home side, who host the Ospreys in Newport on Tuesday, saw Charvis leave the field with a 71st-minute knock, but they rounded off the night in style.
Thomas made a delightful break in midfield, and, although his pass was fumbled, the ball fell kindly to Fussell who crossed in the corner.
Dragons coach Paul Turner:
"That was a hell of a performance with so many players out and after so many games in a short space of time.
"We're a young squad and we're building, but now we have to get up for the Ospreys on Tuesday and a play-off game to come.
"We'll look at the injury situation, but hope to put on a real show against the Ospreys.
"They won't find it easy and don't have a good record at Rodney Parade, but they have to win if they want any chance of the title."
Dragons: Morgan, Fussell, Emerick, Maule, A. Brew, A. Thomas, Walker, Black, Jones, Harrison, Gough, Charteris, Bearman, Owen, Charvis.
Replacements: P. Dolman for Morgan (40), Wyatt for A. Brew (42), Baber for Walker (68), Daly for Jones (68), Hall for Charvis (71). Not Used: Corsi, Lydiatt.
Connacht: Connacht: Duffy, Yapp, Riordan, McHugh, McPhillips, Warwick, Keane, Wilkinson, Fogarty, Knoop, Gannon, Farley, J. Muldoon, Rigney, Ofisa.
Replacements: Robinson for Yapp (61), Durcan for Warwick (50), Flavin for Fogarty (61), Loughney for Knoop (50), Swift for Farley (68), McGowan for Rigney (68). Not Used: Hearty.
Referee: Malcolm Changleng (Scotland)