"Not a great decision that one," injured captain Michael Clarke posted on Twitter.
It is exactly the type of howler that led to the development of the Decision Review System (DRS) six years ago.
However, India mistrust DRS and it will not be used in the ongoing four-test series.
Gould raised the ire of Shikhar Dhawan in the first test, raising his finger when a bouncer clipped Dhawan's arm en route to Haddin.
DRS could also have saved Ajinkya Rahane in the first test, with the batsman incorrectly given out caught at short leg by umpire Marais Erasmus.
Centurion Murali Vijay powered India to a score of 311-4 at stumps on a day of injuries, high humidity and hot-and-bothered Australian bowlers.
Vijay's 144 gave India the perfect platform to have a serious tilt at winning the Gabba test and squaring the series at 1-1.
The opener was dropped on 36 and 102 - both times by Shaun Marsh off the bowling of Mitchell Johnson, who struggled in the heat and managed 15 overs.
The hosts had far greater worries.
Mitch Marsh tweaked his hamstring while bowling the second over after lunch and didn't return to the field.
Debutant Josh Hazlewood was unable to complete his first over with the second new ball, having also been taken off earlier in the final session for assessment.
Mitchell Starc was clearly distressed by the heat during the second-session drinks break, leaving the park alongside team doctor Peter Brukner.
Starc returned to the attack, but every one of Australia's bowlers was well and truly cooked after a long day in the field.
Even Vijay, who batted for five and a half hours, cramped late in his innings and reined in the running between the wickets.
He eventually fell charging Nathan Lyon, Haddin snaffling an edge and also having enough time to take off the bails.
The damage had been done.
It was the equal highest test score at the venue by an Indian.
He was only the 10th foreign opener to face 200 balls or more in an innings at the Gabba.
The hosts had two overs with the second new ball, but failed to create a breakthrough with Ajinkya Rahane finishing 75 not out and Rohit Sharma on 26.
Vijay backed up MS Dhoni's decision to bat first, continuing his strong form after scoring 53 and 99 in the first test.
Johnson made life uncomfortable for Vijay with a salvo of short stuff in the morning. Vijay looked particularly ungainly while fending a bouncer away during Johnson's second over, but the ball popped up over short leg Chris Rogers and fell safely. But he put on a 56-run opening stand with Shikhar Dhawan - the best effort by a touring side in a Brisbane test since 2003.
