ACTXI went into the days play chasing Australia's first innings total of 272 with just six wickets in hand after losing Mack, Jensen, McGrath & Osborne in the final session of day one.
Jess Jonassen was run out by Elyse Perry early on day two, with Angela Reakes next out to the crease in perfect spring conditions at Manuka Oval.
Reakes brought up her half century with ease, hitting seven fours in an impressive display from the 26 year old.
Kapp and Reakes went on to put on a 112 run partnership, with Reakes celebrating her century just before the dinner break.
With ACTXI 12 runs ahead of Australia, skipper Erin Osborne declared at 7-290 and sent Australia back out to bat with Reakes on 103 not out.
Marizanne Kapp was also unbeaten on 61.
Nicole Bolton and Alyssa Healy opened the batting for Australia, and were beginning to look settled when Belinda Vakarewa struck, dismissing Healy for 27.
Australia finished the days play on 2-126 with Elyse Villani and captain Rachael Haynes at the crease.