Laubser impressed against the tournament favourite and had O’Brien in all sorts of trouble.
O’Brien had only good things to say about his younger opponent following his hard-fought victory.
“Brandon is a real talent. He had me troubled out there today, he played nice, loosely with loads of confidence, he hit his backhand particularly well and had me worried,” O’Brien said.
After winning the first set 6-4, O’Brien had match point at 5-4 in the second set on the Laubser serve.
Laubser saved match point, held serve then broke the tentative O’Brien serve which gave him the second set.
In the final set O’Brien broke early to lead 3-1 but Laubser promptly broke back and it was only in the eleventh game that O’Brien managed to find his groove on the return and break Laubser then hold for the match.
O’Brien will now face unseeded Michael Grant of the United States in the quarter finals. Grant shocked sixth-seed Jacob Adaktusson of Sweden 0-6 7-6 (4) 7-5.
Second seed Tucker Vorster of South Africa also had to battle over three sets to beat Juan Cruz Estevarena 6-1 3-6 6-3, while his compatriot Fritz Wolmarans had it easier beating Ronak Manuja of India 6-3 6-2.
Unseeded Nik Scholtz also needed three sets to beat unseeded Brazilian Yuri Andrade 6-1 5-7 6-2 to set up a quarter-final clash with fellow Davis Cup team-mate Ruan Roelofse.
The other players to reach the last eight were fifth-seeded Stefano Napolitano of Italy and seventh-seeded Milos Sekulic of Sweden.
In the women’s singles top seed Chanel Simmonds was in devastating form losing only one game in her 56 minute 6-0 6-1 whipping of fellow countrywoman Caitlin Herb.
Simmonds will now face Pretoria junior Ilze Hattingh, who was a 6-2 6-2 winner over fellow South African junior Zani Barnard.
Unseeded South African Lenice van Eyk earned her first Futures quarter-final berth after she beat Lee Barnard 3-6 3-6.
Van Eyk will play second-seeded Clothilde De Bernardi of France who battled past Ani Vangelova 6-4 7-5.
Natasha Fourouclas, last week’s Futures 1 finalist, had no trouble against Nadine De Villiers, winning 6-2 6-1 and now will meet seventh seeded American Stephanie Kent for a place in the semi-finals.
Third seeded Madrie le Roux had to come from behind to beat unseeded Vanja Klaric of Serbia 2-6 7-5 6-3.
Le Roux will play Nicole Dzenga of Zimbabwe for a place in the last four.