The Blues were eight points down at the break but took the lead after the restart when Patchell converted following a Joaquin Tuculet try.
Connacht pegged them back when Aly Muldowney touched down with ten minutes remaining but Tuculet went over for his second try of the game and Patchell kept his nerve under pressure to convertwell beyond the 80-minute mark.
And while the Welsh fly-half refused to take all the credit for the win he applauded Cardiff's ability to remain calm in a frantic final passage of play.
"It was great composure from the boys because we didn't get anything we wanted on the field in the first half. We were absolutely awful and there were a few stern words at half time," he said.
"To be fair to all of them, it was great composure at the end to keep going, not panic, not throw any silly passes or silly offloads.
"I'm just grateful that Tucs (Tuculet) got a little bit closer to the posts to try and make the conversion easier.
"It's pleasing to knock over the winning kick but the important thing is we have come away as a team with a victory and nothing else other than a victory was good enough.
"We dogged it out last week against Edinburgh and we have done it again tonight.
"I think maybe Chief (Dale McIntosh) and Johnsey (Paul John) would have been happier if we had won a bit prettier and hadn't left it to the last minute, but a win is a win that is four points."
But despite Cardiff's wild celebrations on the final whistle, Patchell insists they have their eyes firmly set on the next game against Ulster.
"We are pleased with the win, but let's not get carried away," he added.
"We have two on the bounce now and have week off now before we come back in to prepare for Ulster.
"These last two weeks have been great but we are not thinking we are world beaters. We have beaten two tough sides, but there is work to be done before we are the finished product."
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