"Nice to be back and contributing," Head told Channel 7. "I was really conscious of making the right decisions - attacking the right balls, defending the right ones, being hard to get out. I felt like I came into this test ready to go."
Labuschagne counterpunched the pace of Chris Woakes (1-50) and Mark Wood (1-79) by clobbering nine boundaries before getting dismissed in a bizarre fashion just before the first session.
Labuschagne was clean bowled in an unusual style when he appeared to slip in the crease and Broad had the middle stump knocked back with the batsman falling over on his knees while going way across his stumps.
But Head and Green continued to prosper against Wood and Woakes in a dominant middle session which yielded 130 runs. Head played some exquisite drives on both sides of the wicket, particularly in front of square as he hammered 12 boundaries before raising his century by cutting Woakes to backward point for two runs.
However, Head fell a ball later after reaching his hundred when he lobbed a gentle catch to mid-on. Green didn't have trouble with the pace before he finally fell to a trap set by captain Joe Root as he pulled Wood's short delivery straight to Crawley who was perfectly stationed at deep mid-wicket.
Earlier, Robinson and Broad made most of the favourable English-like overcast conditions and had Australia in early trouble.
Broad troubled openers David Warner and Usman Khawaja as he bowled three successive maiden overs before Warner edged Robinson to Crawley and fell for a 22-ball duck.
Khawaja, the twin century-maker in Sydney, also couldn't negotiate the seam of Broad and edged to slip after scoring six runs before Robinson found the thick outside edge of Steve Smith (0) as Australia slipped to 12-3 in its first innings inside the first 10 overs.
England's wholesale changes included Jonny Bairstow, who sustained a thumb injury while helping England salvage a draw in Sydney, and wicketkeeper Jos Buttler (broken finger).
England also appeared to have run out of patience with out-of-form opener Haseeb Hameed, while Jimmy Anderson and Jack Leach were also omitted.