Tries from each of the back three, Tiernan O'Halloran, Niyi Adeolokun and Matt Healy fired them to victory, while Muldoon was named man of the match for his efforts in the Edinburgh sunshine.
For a club that has endured many tough times over the years, it marked a wonderful end to a dream season under Pat Lam, with Muldoon admitting there was a feeling of destiny as the players arrived at the ground.
He explained: "It was phenomenal, we came in to a sea of green and the Fields of Athenry. We were all walking in with shivers down our spine. That's probably destiny.
"It's absolutely phenomenal. You dream of days like this and being part of days like this but it hasn't sunk in yet. I'm delighted for the lads.
"We spoke all week about wanting to go out there and perform and do what we've done all year and I think we did that. I'm delighted for everybody.
"We all watch sport because we know on any given day, anybody can win. Sport can be beautiful but it can also be very cruel. This could have been cruel, but we wanted to play like we've been playing."
Even this season Connacht have had to deal with some difficult moments, in particular a heartbreaking loss to Grenoble in a Challenge Cup quarter-final.
But while their attacking game plan may have played a part in their downfall on that occasion, Muldoon was convinced that sticking to their guns would get the reward in the long run. And so it proved.
"Pat's been hammering it home, I've been hammering it home," he added.
"Don't fall back into habits of old. Some people in the crowd were probably thinking about Grenoble. We've learned lessons. We didn't panic like we did over there.
"We have a game plan and no matter what people say we stick to it wholeheartedly and we've bought in massively. You've got to credit the lads."
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