Niall O’Connor opened the scoring after two minutes for the visitors with a penalty but full-back Ben Blair soon responded for the Blues, kicking two penalties in quick succession.
Tiernan O’Halloran crossed for the game’s first try, but two further Blair penalties edged the Blues into the lead at the break to the delight of the home support.
And it was Blair who opened the second-half scoring, slotting a 56th-minute penalty to hand the Blues a five-point advantage at 15-10.
Prop Sam Hobbs then crossed for the Blues’ only try at the start of the fourth quarter to secure his side’s seventh victory of the season.
Blair’s straightforward conversion took his personal tally to 17 points and, although Dave Moore claimed a late consolation and a bonus-point for Connacht, the Blues were good value for their fourth win in five games.
