22-15 victors at the Galway Sportsground.
Matt Healy's try, and five points from the boot of Miah Nikora, had given Connacht the advantage.
But despite Robbie Henshaw's try early in the second half for the hosts, the Blues were not about to give in.
Lewis Jones, Dan Fish and a penalty try - combined with Gareth Davies' seven points from the kicking tee - ensured Cardiff made it four wins on the spin in the RaboDirect PRO12.
But McIntosh was left a little frustrated with how long it took his side to hit top gear.
"We made fundamental errors in the opening half but once we kept the ball and went through the phases then we got the points," said McIntosh.
"We knew it would be hard because this is a tough place to come and we were out of it in the first half."
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