Di Bartolo scrambled home a 71st minute winner as despite their numerical disadvantage Brisbane were still on top for much of the contest.
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Hayley Raso's jinking run almost manufactured an equaliser for Brisbane in the 29th minute but the lively attacker was unable to make a clean connection under pressure.
The hosts seemed unconcerned about being down to ten as they continued to apply pressure in search of a fourth straight win, though FIFA Women's Player of the Year nominee Nadine Angerer was forced into late first-half action when she was quick off the line to snuff out a potential 1v1.
Brisbane came close to an improbable opener within minutes of the restart when an adventurous surge forward by Clare Polkinghorne was rewarded, but the skipper drove her finish into the crossbar.
Angerer again proved her influence with a sharp save from Tegan Riding after Snez Veljanovska sent the substitute clean through on goal.
The German 'keeper was unable to repeat her heroics in the 74 minute though as Riding turned provider to slip Moore in behind, whose squared toepoke was eventually scrambled home by Daniela Di Bartolo.
The home side had a chance to seal a point in the 85th minute when Hayley Raso sliced through the Lady Reds' midfield to feed Amy Chapman wide on the right, but her shot to the near post ignored a free Raso for the cutback and was seen wide by Melissa Barbieri.
Brisbane Roar: 1. Nadine ANGERER (gk), 2. Laura ALLEWAY, 3. Amy CHAPMAN, 4. Clare POLKINGHORNE, 5. Brooke SPENCE, 7. Kim CARROL, 8. Elise KELLOND-KNIGHT, 9. Larissa CRUMMER, 10. Katrina GORRY, 11. Vedrana POPOVIC, 16. Hayley RASO.
Bench: 20. Kate STEWART (gk), 6. Joanne BURGESS, 14. Natasha WHEELER, 19. Ayesha KIRBY.
Adelaide United: 1. Melissa BARBIERI (gk), 3. Alexandra GUMMER, 5. Jessie WHAREPOURI, 7. Rachel QUIGLEY, 9. Lisa-Marie WOODS, 12. Daila-Tais BORG, 14. Jayah BROWN, 15. Jenna McCORMICK, 17. Tiarn POWELL, 21. Snez VELJANOVSKA, 23. Kristy MOORE.
Bench: 20. Kelly BARLTROP, 4. Tegan RIDING, 6. Laura STOCKDALE, 19. Daniela DI BARTOLO.