Pat Lam's men had endured eight successive defeats since beating Zebre in round 1 back in September, falling to the bottom rung of the league table.
But despite going 8-0 down to the Dragons inside 16 minutes, Connacht - helped by a dominant scrum and lineout - fought their way to a gutsy three-point win in Galway.
Daniel Evans' early unconverted try was the difference between the sides at the break, the wind-backed Dragons establishing a 8-3 interval lead with Jason Tovey and Dan Parks swapping penalties.
Two more successful kicks from Parks and Tovey followed and Lyn Jones' side maintained their 11-6 lead despite losing prop Owen Evans to the sin-bin.
But Connacht produced the stronger finish with Parks setting up replacement Fionn Carr for a 75th minute try and then nailing his vital drop goal with just over a minute left.
The sixth-minute withdrawal of centre David McSharry, who picked up an ankle injury, forced Connacht to shuffle their back-line with Carr introduced and both Robbie Henshaw and Gavin Duffy making positional switches.
It was Henshaw's missed tackle that allowed Ross Wardle to break through midfield in the eighth minute and tee up full-back Evans for his five-pointer.
Tovey, who had missed an earlier penalty, was back on target with a 16th minute penalty as the Welsh region kept pressing with a strong wind at their backs.
However, Connacht then used their solid scrum to build some momentum, with youngsters Eoin McKeon and Michael Kearney both prominent in the set pieces.
A scrum penalty allowed Parks to knock over a 33rd minute penalty and as the strength of the wind dropped noticeably, Connacht's forwards exerted more influence with the visitors' chances to attack curtailed.
The gap was down to just two points after Parks potted a penalty early in the second half, punishing young lock Cory Hill for being caught offside.
A good spell of possession saw the Dragons hit back with Tovey left-footing a long range penalty, but a yellow card was looming for the visitors as their own penalty count increased.
Loosehead prop Owen Evans was the man to see yellow on the hour mark, referee Alain Rolland sin-binning him for a push on Jason Harris-Wright. However, the home side suffered further frustration when Parks failed to convert the resulting penalty.
The Dragons kept it simple during a weather-beaten final quarter, with number 8 Toby Faletau leading by example in terms of his sharpness on the ball.
But Connacht - driven on by man-of-the-match John Muldoon - pounced for a levelling try with five minutes left, Parks' deft cross-field kick being dotted down by the unmarked Carr out wide.
The former Scotland international narrowly missed his conversion attempt to the left, however, and Connacht needed to work their way downfield to set up a second shot at the posts for him and thankfully for the home support, he delivered the goods.
No. | Name | T | C | D | P | |
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15 | Robbie Henshaw |
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14 | Gavin Duffy |
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13 | Eoin Griffin |
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12 | Dave McSharry |
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11 | Matt Healy |
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10 | Dan Parks |
1D |
2P |
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9 | Kieran Marmion |
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1 | Brett Wilkinson |
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2 | Jason Harris-Wright |
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3 | Nathan White |
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4 | Mick Kearney |
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5 | Craig Clarke |
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6 | John Muldoon |
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7 | Jake Heenan |
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8 | Eoin McKeon |
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16 | Dave Heffernan |
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17 | Denis Buckley |
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18 | Rodney Ah You |
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19 | Andrew Browne |
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20 | George Naoupu |
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21 | Paul O'Donohoe |
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22 | Jack Carty |
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23 | Fionn Carr |
1T |
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No. | Name | T | C | D | P | |
---|---|---|---|---|---|---|
15 | Dan Evans |
1T |
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14 | Will Harries |
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13 | Pat Leach |
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12 | Ross Wardle |
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11 | Hallam Amos |
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10 | Jason Tovey |
2P |
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9 | Richie Rees |
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1 | Owen A. Evans |
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2 | Sam Parry |
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3 | Nahuel Tetaz Chaparro |
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4 | Andrew Coombs |
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5 | Cory Hill |
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6 | Lewis Evans |
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7 | Nic Cudd |
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8 | Taulupe Faletau |
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16 | T.Rhys Thomas |
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17 | Hugh Gustafson |
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18 | Dan Way |
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19 | Matthew Screech |
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20 | Ieuan Jones |
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21 | Wayne Evans |
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22 | Steffan Jones |
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23 | Ashley Smith |
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