The Irish hosts opened up a commanding 15-3 lead in the RaboDirect PRO12 encounter with tries from Matt Healy and Robbie Henshaw.
But a dramatic final 25 minutes saw Blues wrestle back control of the clash with quick-fire scores from Lewis Jones and a penalty try after a powerful scrum show.
Full back Dan Fish sent Blues further ahead to leave stunned hosts Connacht shell-shocked and earn praise from McIntosh for the manner in which the team
The result was a fourth successive win for Blues in the league and means they can finish no lower than eight in the standings with a final game away at Scarlets to come next weekend
"This is a tough place to come and win," said McIntosh. "We're going to enjoy that result because I have got huge respect for Connacht.
"They have obviously got ambition bringing Pat (Lam) here and he has got major plans for the province.
"I think they are going to be very successful, so to come here and win and really show our steel to comeback was a real positive.
"We made some fundamental errors and lacked continuity in the opening 50 minutes.
"But once we kept hold of the ball for longer and went through the phases we started picking up points."