“I hope it’s going to be a dominant position, we have played well over the last two days,” said Head.
“It’s nice to contribute to that, I felt like I played well personally. It’s nice to make use of some chances, play well and put us in a good position.”
In reply, India struggled as the sun went down with KL Rahul lasting just 10 balls before Cummins sent a short one to the ribs and he gloved to Alex Carey behind the stumps.
Yashasvi Jaiswal, out for a golden duck in the first innings, made 24 this time, but he had no answer to Boland, whose first ball angled away and took a nick to Carey.
Boland stunned superstar Virat Kohli (11) in similar fashion, with Carey holding his third of the night to leave India tottering at 66-3.
Shubman Gill was next to go after a determined 28, with his middle stump removed by Starc, before Cummins bowled Indian captain Rohit Sharma for six.
India bowling coach Morne Morkel admitted his team had their work cut out, and praised Head’s contribution.
“Head is a guy that is looking to score, as a bowler he puts you under pressure,” he said.
“So your execution gets tested.
“When he came to the crease we bowled really well, I thought we could knock him over, but credit to him, he got through that phase then put the pressure on us.”
When play started, India got an early breakthrough with Nathan McSweeney adding just one to his overnight 38 before being beaten by Jasprit Bumrah’s sheer pace, nicking to wicketkeeper Pant.
Bumrah and Pant then combined to remove Steve Smith (2) four overs later, with the former Australia skipper shaking his head in disbelief after falling into a similar trap.
At the other end, Labuschagne kept his focus, rediscovering the magic that has recently eluded him with calls mounting for him to be dropped.
But the tenacious number three, who resumed on 20, silenced the doubters by reaching his 21st Test 50 off a patient 114 balls in a big confidence booster.
With the landmark behind him he began playing more freely before a brilliant catch from Jaiswal at gully ended his reign and Head took charge.
Head adopted his usual aggressive posture, blasting two sixes off spinner Ravichandran Ashwin as he reached his half-century from 63 balls.
He then ramped up the attack, racing to his second 50 off just 48 deliveries to clock an eighth Test ton, riding his luck along the way after being dropped on 76 by Mohammed Siraj.
Mitchell Marsh briefly hung around before feathering to Pant on nine off Ashwin while Carey contributed 15 before he too got a faint edge to Pant, this time off Siraj.
Head finally succumbed to the rampaging Siraj, clean-bowled, with the pair involved in a fiery exchange in the aftermath after the Indian quick gave the hometown hero a send-off.
