In-form Connacht - whose only defeat this season was a late 35-33 loss at the Scarlets in round two of the league - started well in front of the 11,000 crowd, Carr looking particularly dangerous with two scintillating breaks.
Vintage Blues on Sunday's Scrum V
Fly-half Keatley opened the scoring with a penalty that was soon cancelled out by Blues opposite number Parks.
The Scotland international then calmed home nerves, taking his side clear with a second penalty followed by a drop-goal.
The Blues' creative inspiration Laulala then received the ball just outside the Connacht 22 and ripped their defence apart with a sublime piece of skill.
The former New Zealand All Black dummied a pass to Ben Blair, then stepped sweetly between the flailing Keatley and Niva Ta'auso to slide in under the posts for a converted try.
Connacht mounted a sustained assault on the Blues line as the first half drew to a close, Carr again to the fore, but a knock on left the home side's 16-3 lead intact at the break.
Keatley landed his second penalty to reduce the deficit at the start of the second period, before fine defensive work from Gavin Duffy denied Chris Czekaj a try after a break-out from his own half, sparked by Blair.
Keatley blew a straightforward penalty chance as the game Irish side continued to press.
But any fears felt by the home fans disappeared as Parks landed another kick then Halfpenny booted a long-range penalty from just inside his own half.
The Blues have now won all eight of their games against Connacht, who have just one win from their last 23 visits to Wales.
Scrum V goes golf crazy
"We have to give Connacht credit but we caused ourselves problems with our lack of accuracy, especially at the set piece," said Blues coach Dai Young.
"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."
Laulala added: "We're doing something right - we're not playing great rugby but we're winning."
Cardiff Blues: Blair, Halfpenny, Laulala, Hewitt, Czekaj, Parks, Cooper, Yapp, R. Williams, Filise, B. Davies, Jones, Paterson, Warburton, Rush. Replacements: Sweeney for Laulala (75), Shanklin for Hewitt (37), Baller for Cooper (78), Jenkins for Yapp (60), Dacey for R. Williams (71), Andrews for Filise (60), Tito for Jones (60), Pretorius for Paterson (55).
Connacht: Duffy, Nathan, Ta'auso, Matthews, Carr, Keatley, F. Murphy, Wilkinson, Flavin, Hagan, Swift, A. Browne, McCarthy, Ofisa, McComish. Replacements: Fanning for Nathan (79), Nikora for Matthews (48), Willis for F. Murphy (71), Loughney for Wilkinson (53), D. Murphy for Flavin (78), Sweeney for Hagan (70), Upton for A. Browne (65), O'Connor for McComish (40).
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.