Brandon representing Australia at the games finished 10th in the qualifying stage clearing 2.29m on his third and final attempt.
His jump was just 2 cm below his personal best which he recorded at the Commonwealth Games in 2014.
After his qualification, Brandonm, 22 said: "When (Bahamas athlete) Trevor Barry cleared it I knew it was getting tight because he was below me.
"It was the last jump of the night - everyone was going home after that.
"And I thought, 'I don't want to end it here' so just gave it everything."
He further added: "I was just about to jump and fed off that a little bit,' said Starc, a finalist at his first world championships in Beijing last year.
"It was a big night. I'm glad I was a part of it."
Before his event yesterday his big brother and Australian cricketer Mitchell Starc had tweeted wishing Brandom best wishes.
His tweet read:
Brandon replied tweeting:
So overwhelmed with the amount of support from close and far. Thank you all so much. Time to recover and go bigger in the final!— Brandon Starc (@Brandonstarc93) August 15, 2016
Earlier, Mitchell had said: "I'm pretty excited and proud of the younger brother to represent his country in the Olympics."
Mitchell Starc is currently in Sri Lanka as Australia are touring for 3 match test series. Sri Lanka have already won the series leading 2-0. The third and final test is ongoing.