Connacht fly-half Ian Keatley landed his second penalty to cut the gap to 16-6, and missed a third shot at the posts as Cardiff struggled to see off the visitors.
But with replacements Andries Pretorius, Gethin Jenkins and Paul Tito steering the hosts back on track, two more penalties from Dan Parks and Leigh Halfpenny wrapped up the points for David Young's side.
Connacht had shown plenty of spark in the opening stages, with tricky winger Fionn Carr threatening to find a way to the try-line.
Keatley opened the scoring in the fifth minute, yet the Blues gradually found their rhythm and a classy converted try from Laulala gave them a 13-point advantage, with Parks kicking the rest of the first half points.
Acknowledging that it was a less-than-impressive display from his side, Young said: "We have to give Connacht credit but we caused ourselves problems with our lack of accuracy, especially at the set piece.
"A bit of magic and Dan Parks' boot made the difference. It's a win but it shows how far we've come that we can really play poorly and win.
"It's a disappointed dressing room but we know we have to improve for the Heineken Cup, Edinburgh will be rubbing their hands watching that."
Young handed fit-again scrum half Gareth Cooper his first start of the season, with former All Black Laulala returning from injury in the centre.
Recovered from a knee injury, Xavier Rush captained the side from number 8, while the selected front row included Rhys Williams at hooker and John Yapp at loosehead prop.
Connacht coach Eric Elwood made two changes to the team that drew 15-15 with Ulster. Adrian Flavin started at hooker, taking over from the rested Sean Cronin, and Andrew Browne came in for Bernie Upton in the second row.
Connacht looked composed from the off and willing to attack from deep. Carr threatened twice - his initial break was ended by a Halfpenny tackle and then a surging run through the middle gave the visitors a great platform in the Cardiff 22, only for Flavin to knock on.
That early pressure yielded a penalty for a binding offence from Yapp, and Keatley's crisp strike from the left opened the scoring in the fifth minute.
Connacht's good work was undone by Parks who levelled matters two minutes later, but the Scotland international pushed a second penalty effort to the right of wide, after a counter attack from winger Halfpenny.
The Blues were beginning to see more and more ball and when their forwards won a penalty off a scrum, Parks fired them ahead courtesy of a right-sided kick.
Connacht winger Troy Nathan did just enough to put off his fellow New Zealander, Michael Paterson, as the Blues tried to exploit a huge overlap on the right.
Paterson's knock on handed possession back to Connacht, who also had Nathan to thank as he covered a dangerous crossfield kick from Parks shortly afterwards.
Cardiff remained in Connacht's half for much of the second quarter, and Parks rewarded his forwards by picking off a drop goal to make it 9-3.
Halfpenny displayed his defensive skills again as his cover tackle prevented a try in the left corner for Keatley, who was alert to a loose ball that broke from a Cardiff ruck.
Sam Warburton then took the wrong option as he launched a chip and chase attack down the right, with Connacht full-back Gavin Duffy outpacing him to the ball.
But the Blues, with Rush carrying well up front, were getting closer and closer to nabbing the first try and it arrived 10 minutes before half-time.
Cooper and Parks used ruck ball to set Laulala up on the left. The busy centre brilliantly dummied and jinked past Niva Ta'auso and Keatley before sidestepping around the covering Frank Murphy and sailing over beside the posts.
Parks converted what proved to be the only try of a closely-fought contest. Connacht tried to response. They turned down a late shot at the posts, in favour of a quick tap penalty, but a handling error spoilt a promising move in the Cardiff 22.
The Blues' 16-3 interval lead was cut by Keatley, just four minutes after the resumption. Soon after, Duffy again showed his pace and awareness to foil Chris Czekaj as the Cardiff winger raced after his own chip kick close to the touchline.
Scoring chances were few and far between in the wet conditions, and Parks had a drop goal attempt charged down before Keatley missed his first place-kick of the night.
Neither side could garner much momentum off set piece ball and it was in broken play that most of the excitement was created.
There was little room to create opportunities and it was no surprise when Cardiff took the option to kick themselves to victory, in front of an attendance of 11,058.
Parks booted a 69th minute penalty and then Halfpenny followed up with a 51-metre effort to clinch the win - the Blues' 12th triumph in their last 13 competitive games.
Connacht will be annoyed to have missed out on the losing bonus point. Hooker Flavin was held up just short of the try-line in the closing stages, and they should have converted at least one of their first half chances.
|Cardiff Blues Score Card|
|Connacht Rugby Score Card|