The early damage was done during an impressive 20 minutes of forward dominance which saw tries from Muldoon and Rodney Ah You - the first from a Dragons scrum and the second from a line out.
Dragons improved after the break but while Tom Prydie crossed the whitewash, Connacht added two further tries from driving mauls through Muldoon and Michael Swift to cement victory.
Despite the win, it was the Dragons who burst out of the traps winning a turnover at the breakdown inside a minute leaving Jason Tovey to pop over a penalty for a three-point lead.
Prydie then had a chance to extend their lead four minutes later but he put his long-range effort wide.
But from then on, Connacht turned the screw up front, with the TMO called into action on 12 minutes when their first scrum near the try line barged over.
However Kieran Marmion was adjudged to have played the ball early, with Dragons' Nic Judd diving on the ball, with the penalty awarded instead to the home side.
But it would prove to be a short reprieve for the Dragons who saw their scrum disintegrate on 16 minutes with Muldoon getting the last touch, Dan Parks adding the extras.
And with Dragons' lock Robert Sidoldi finding himself in the bin for constant infringement at the line out, Connacht's forwards again showed the hand with Mick Kearney sending in the line out ball and the pack again delivering.
Ah You dived on the ball over the line, and with Parks adding his second conversion, the visitors found themselves 14-3 up with 23 minutes gone.
Struggling to get a foot in the game, the Dragons changed their entire front row and they finally managed to launch an attack through Jack Dixon but Eoin McKeon got back to clear the danger.
Reinvigorated by the half-time break, Dragons came out with more purpose after the restart, bringing on Taulupe Faletau on 51 minutes for his first appearance since returning for Wales duty.
Having won a penalty, the hosts opted to kick to the corner on 52 minutes but they were unable to find a way through from the line out, eventually losing possession.
Connacht conceded a penalty on 62 minutes but Parks could not find his range with the Irish side making them pay almost immediately with the pack again driving over.
Muldoon was the man to get the try, although replacement Miah Nikora missed the conversion for 19-8.
Dragons were not prepared to roll over and finally added to their first-minute penalty by capitalising on Darragh Leader's yellow card to send winger Prydie over in the corner. Tovey failing to make the conversion.
Marmion went looking for the bonus-point win for Connacht with five minutes remaining, breaking towards the corner but Dragons eventually got back to clear.
But they were not to be denied, as another driving maul saw the same result for Connacht with Swift touching down. Nikora missed the conversion but it did not matter as Connacht march on.
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Newport Gwent Dragons Score Card | |||||
Name | Tries | Conv | Pen | Drop | Pts |
---|---|---|---|---|---|
Tom Prydie | 1 | 5 | |||
Jason Tovey | 1 | 3 | |||
Total | 1 | 1 | 8 |
Connacht Rugby Score Card | |||||
Name | Tries | Conv | Pen | Drop | Pts |
---|---|---|---|---|---|
Michael Swift | 1 | 5 | |||
Dan Parks | 2 | 4 | |||
John Muldoon | 2 | 10 | |||
Rodney Ah You | 1 | 5 | |||
Total | 4 | 2 | 24 |
|