Danie Poolman and Willie Faloon both crossed in the first five minutes for the visitors.
The Blues fought back with tries from Harry Robinson and Robin Copeland but Faloon grabbed a second in the second-half to snatch the victory.
It took the Galway-based outfit just two minutes to open the scoring as they caught Cardiff cold in freezing conditions.
After dominating the opening exchanges Connacht worked an overlap and sent Poolman over in the corner.
Miah Nikora missed the conversion but the visitors soon stretched their lead.
Brian Murphy sliced through the Blues midfield and although caught by the covering defence he offloaded to Faloon, who cantered home.
Nikora made no mistake to add the extras but Patchell responded and the Blues launched their fight-back.
They dominated the remainder of the half and following a sustained period of pressure Patchell sent Robinson diving over the whitewash before Nikora hit-back.
The Blues made a bright start to the second-half and treatended to manufacture a second-try.
Lewis Jones went agonisingly close but Jason Harris-Wright cynically off-side and sent to the sin-bin as a result.
Patchell slotted the ensuing penalty but Nikora was also on target with the boot as Connacht clung on.
But the Blues soon went in front for the first time. Scott Andrews made the initial break and, within minutes of coming on, Liam Davies raced down the touchline and flicked an offload inside, which bounced to Copeland.
Patchell converted but the hosts’ lead did not last long as Faloon crossed from the back of a solid scrum.
Nikora failed to add the extras and Patchell reduced Connacht’s lead to a single point.
But Nikora restored Connacht’s four-point advantage and despite a late rally they hung on for the victory – their first over the Blues since 2009.
