They had trailed 17 v 6 at the break but fought back with two tries in the space of five second-half minutes.
Connacht got off to the perfect start with wing Tiernan O’Halloran scoring after just two minutes for the hosts.
Dan Parks then opened the Blues’ account with a penalty of his own before the two fly-half’s exchanged further shots at goal.
Connacht then grabbed their second try just before the break, Mike McCarthy crashing over from a rolling maul.
Whilst the Blues went into the break 17 v 6 down hey did look the brighter in the backline and it took them just five second-half minutes to snatch the lead back.
First Alex Cuthbert divided over after a line break from Casey Laulala and then the former All Black scored himself just four minutes later.Â
The Welsh side then lost captain Paul Tito to the sin-bin and replacement fly-half Miah Nikora leveled the scores from the resulting penalty for Connacht. But the Blues began controlling preceding and Parks responded with a penalty and a drop-goal to secure the victory.
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