The South African pair struggled at the start of the 72-hole examination, but rallied over the weekend to tie for 28th on nine-over-par 297.
Bregman carded rounds of 75, 80, 72 and 70, while Strauss posted 75, 78, 71 and 71 to finish in the bus alongside Ladies European Tour winner Rebecca Artis and Symertra Tour champion Breanna Elliott from Australia, as well as Fiona Puyo, Budsabakorn Sukapan from Thailand, Norway’s Caroline Martens and American Ginger Howard.
A total of 85 players from the 195-strong field qualified for Final Stage and Bregman and Strauss will join compatriot Ashleigh Simon at the LPGA International Golf Course from 2 – 6 December.
Simon, a two-time Ladies European Tour winner and four-time Sunshine Ladies Tour champion, kept her card for next 2016 season, but hopes to improve her ranking for 2016 with a top 20 finish at Final Stage.
Only players in the top 20 finish receive Category 12 cards for the LPGA Tour, while the players that finish between 21 and 45 will gain conditional cards.
Ladies European Tour winner Connie Chen and fellow South African Ulrika van Niekerk both failed to make the cut, however, all the players who missed the cut but completed 72 holes automatically received Symetra Tour status for 2016.
American Nelly Korda fired a final round 69 to win the Stage II qualified at four under, but the win also marked the end of the qualifying road for medallist from Florida.
The LPGA has a rule requiring members be 18 years old and Korda only turns 18 in July 2016, but prior to the start of Stage I, the 17-year-old Florida amateur petitioned the LPGA for a waiver to go to Q-School in a bid to play the Symetra Tour next year.
Meanwhile Lee-Anne Pace tied for 23rd in the Fubon LPGA Taiwan Championship in New Taipei City, Taiwan, while Monique Smit grabbed a share of 30th in the Hero Women’s Indian Open on the Ladies European Tour. Pace carded round of 75, 70, 70 and 73 to finish on even-par 288, 20 strokes of the pace from New Zealand’s Lydia Ko.
Smit returned rounds of 78, 75 and 75 to finish on 12 over 228, while LET rookie Emily Pederson from Denmark won the event on even-par 216 with a wire-to-wire performance at the challenging Black Knight course at DLF Golf and Country Club in Gurgaon.