That condemned Warriorz, skippered by another Australian Alyssa Healy, to Thursday's playoff against Mumbai Indians for the right to face Delhi in Sunday's final.
Mumbai had beaten Royal Challengers Bangalore by four wickets earlier in the day, but they did not improve their net run rate (NRR) sufficiently to overtake Capitals, who thus merely needed to beat Warriorz to qualify.
Put in to bat in Mumbai Warriorz made 6-138 in their 20 overs, a hard-hitting unbeaten 32-ball 58 from Tahlia McGrath building on Healy's 34-ball 36.
Capitals' Jess Jonassen, who took 1-24, said: "For us to finish top of the table is obviously a huge advantage, we get a few days off and get straight through to the final.
"I'm incredibly proud of the girls and how we've come back from a few setbacks. We've bundles of international experience, some incredible talent within the group and a real family atmosphere.
"One job is done, we're through to that final, but one more big game to go."
Lanning's 23-ball 39 meant Capitals were always ahead of the clock and Alice Capsey (34 from 31, and Marizanne Kapp (31 not out off 31) carried them to victory with 13 balls remaining.
Previously, in Navi Mumbai, Amelia Kerr took three wickets, scored 31 runs, and effected a crucial run-out as Indians ended the group stage with a return to form.
The New Zealander ran out compatriot Sophie Devine, who made 99 in her previous innings, for a second ball duck as Indians beat RCB with 21 balls to spare.
Indians captain Harmanpreet Kaur won the toss for the first time in their eight matches and put RCB in. Three balls later Devine got into a horrible mix-up with Smriti Mandhana and was run out by Kerr from backward point.
RCB were subsequently restricted to 9-125 with Kerr taking 3-22 and English pair Izzy Wong and Nat Sciver-Brunt two wickets apiece. Ellyse Perry and Richa Ghosh top-scored with 29 each for RCB who end their disappointing campaign with two wins from eight matches.
With a playoff place already certain Indians attacked the target with gusto, seeking to improve their NRR.
The 50 came up after 31 balls with an over from Perry having gone for 12, but then wickets began to tumble. After Yastika Patil went for a 26-ball 30 Megan Schutt (1-19 off four) dismissed Hayley Matthews for 24 off 17. When Perry (1-18 off two) bowled Kaur Indians were 4-74.
Kerr steadied the innings and led Indians to victory, her unbeaten 31 coming off 27 balls.
