Pat Lam's side earn a win away in Wales with the help of Matt Healy's try and Tiernan O'Halloran's drop goal
Connacht have picked up a 19-13 away victory at Cardiff Blues in the Guinness Pro 12.
Matt Healy's 39th minute try for Pat Lam's side ultimately proved crucial along with a successful conversion from John Cooney giving Connacht hope for the second period.
But the Irish province had to fight back to earn the win in Wales.
Two Gareth Anscombe penalties had Cardiff six points to the good after 20 minutes.
And they stretched their advantage when Nick Williams scored a 28th minute try with Anscombe adding a conversion to leave the scores at 13-0.
But Healy's try on 39 minute proved timely as it arrived just before half time and gave Lam's side some hope for the second half.
John Cooney penalties cut the deficit further and left the teams level heading into the final 15 minutes.
Ireland international Tiernan O'Halloran then made an impact with a drop goal just two minutes from the end to push Connacht ahead and Craig Ronaldson's penalty left six between the sides at the final whistle.
Connacht are in eighth place in the Pro 12 standings, just behind Cardiff.
Connacht's Matt Healy scores his side's first try ©INPHO/Camerasport/Ian Cook
Connacht's Stacey Ili is tackled by Gareth Anscombe of Cardiff Blues ©INPHO/Camerasport/Ian Cook
Connacht's Tiernan O'Halloran is tackled by James Down and Seb Davies of Cardiff Blues ©INPHO/Camerasport/Ian Cook
Connacht's Tiernan O'Halloran receives the Guinness PRO12 Man of the Match award from Cardiff Blues supporters club member Mike Tilley on behalf of Guinness ©INPHO/Camerasport/Ian Cook