Chasing 301, WA were looking shaky after stumbling to 6-239 in the 41st over of Sunday's match
But Cartwright's unbeaten 66 off 49 balls, which featured five fours and three sixes, helped get WA over the line with six deliveries to spare.
Ashton Agar (21no off 27) produced an important cameo in what turned out to be a match-winning 62-run partnership with Cartwright.
WA's bid for a fourth consecutive one-day title was on thin ice following losses to South Australia and NSW.
Given each team plays only seven regular-season matches, a loss to Queensland could have ended WA's hopes of reaching the March 1 final.
But Cartwright's knock has kept WA's hopes of a four-peat alive, with Queensland (two losses, one no-result) facing an uphill battle to reach the decider.
WA paceman Jhye Richardson was named man of the match after taking 3-36 in 9.3 overs in Queensland's total of 300.
Just a reminder Jhye Richardson has mad skills 🤯🤯🤯 — cricket.com.au (@cricketcomau) #OneDayCup pic.twitter.com/AxcUnlszGBOctober 13, 2024
The Bulls were in all sorts of trouble at 4-51 in the 12th over following the departures of Ben McDermott (9), Matt Renshaw (0), Marnus Labuschagne (11) and Jack Clayton (0).
Star opener Usman Khawaja (76 off 80 balls) struck eight fours and a six as he combined with Lachlan Hearne (76 off 81 balls) to steady the ship.
Bowling all-rounder Michael Neser (56 off 36 balls) then provided the late fireworks, cracking six fours and two sixes to give Queensland's total a significant boost.
Richardson was the pick of WA's attack, bowling McDermott in the third over with a delivery that swung back in wildly.
His dismissal of the dangerous Neser later in the innings ensured Queensland's score wasn't bigger.
Cameron Bancroft entered the match desperate for runs after posting twin ducks in the recent Sheffield Shield draw with Queensland.
Neser claimed Bancroft's wicket in both Shield innings, but the WA opener managed to get through the early stages on Sunday before being trapped lbw by Labuschagne for 33.
Sam Whiteman (74 off 67) ensured WA got off to a solid start, and Connolly's 39 off 42 balls lifted the Warriors closer to victory, before Cartwright and Agar finished the job.
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