Conor McPhillips second-half try set up Connacht's first ever defeat of the Blues and the Irish province's first competitive home win since January.
Connacht (3) 13
Blues (3) 9
Pens: Robinson (3)
A poor first half saw Paul Warwick and Nicky Robinson hitting penalties to leave the game 3-3 at the break.
McPhillips' 53rd minute try proved the crucial score and two Robinson penalties were too late for the Blues.
Warwick's eight points included his conversion of McPhillips' touchdown and a clever drop-goal.
An error-ridden opening half saw the Connacht scrum, which had lost loosehead prop Ray Hogan to injury before kick-off, come notably under the cosh.
The home side's shoddy set piece allowed fly-half Robinson to kick Cardiff into a sixth-minute lead, and early on, the visitors looked the more comfortable - especially with nine internationals in their line-up.
Blues boss Dai Young handed competitive debuts to Mike Phillips and Andy Powell, but disappointingly, there was little in the way of attacking ball for either to get their teeth into.
It was Connacht who got closest to making the try breakthrough as nearing the half-hour, David Slemen and Darren Yapp combined to race play into Blues' territory, but the move fell apart.
By that stage, Connacht had levelled. Following the 13th-minute sin-binnings of home flanker John Muldoon and Wales lock Robert Sidoli for an off-the-ball scuffle, Warwick dinked the resultant penalty through the uprights.
After Robinson missed a chance to reply early in the second half, drilling a drop goal shot wide, McPhillips scorched through to outpace two cover men for the corner.
Warwick did well to convert and the Australian held his nerve to kick a 74th-minute drop goal, sandwiched between a brace of Robinson penalties, to keep up Connacht's record of winning every one of their opening league games since 2001.
"I was pleased to be level at half-time as I knew we had the strong wind in the second half," Blues coach Dai Young told BBC Sport Wales.
"But we didn't play smart rugby and it seems we don't know how to win games.
"We were 20-to-30 points better that them and we didn't make it show, we have to address that."
Connacht: David Slemen; Conor McPhillips, Darren Yapp, Keith Matthews, Matt Mostyn; Paul Warwick, Chris Keane; Ray Hogan, John Fogarty, Stephen Knoop,Christian Short, Andrew Farley, John Muldoon, Matt Lacey, Colm Rigney.
Replacements: Chris Venter, Dan McFaland, Ronan Loughney, Michael Swift, Brendan O'Connor, Conor O'Loughlin, Daniel Riordan.
Blues: Nick Macleod; Chris Czekaj, Rhys Williams (capt), Tristan Davies, Craig Morgan; Nicky Robinson, Mike Phillips; John Yapp, Gareth Williams, Martin Jones, Deiniol Jones, Robert Sidoli, Maama Molitika, Robin Sowden-Taylor, Andy Powell.
Replacements: Ryan Powell, Lee Thomas, Matthew Nuthall, Ben Evans, Rhys Thomas, Craig Quinnell, Mark Lewis.
Referee: Andy Ireland (SRU).