The veteran Australian opener stood out with an authoritative 124 -- his sixth hundred in nine Tests at the Melbourne Cricket Ground and his 28th Test century -- as the Australians struggled to 337 for nine at stumps on the opening day.
Openers Hayden and Phil Jaques propelled Australia to a 135-run opening stand, but scoring became progressively harder over the final two sessions.
Hayden believes India will have the worst of the batting conditions over the remaining days of the Melbourne Test.
"I think we've lost a few too many wickets, there's no doubt about that, but in my mind it was a difficult enough wicket and those conditions will be revealed over the next four days," Hayden said.
"The fact is we are facing quite a difficult wicket. It's definitely a par effort (Australia's score), but maybe one or two more wickets down.
"I think it is going to be a wicket that will be definitely hard to score on over the next few days.
"They are going to be slow conditions, they are going to be challenging for run-scoring and I think you will see Australia putting the pressure with good in-out fields and really try to constrict India.
"I definitely think the pitch is going to deteriorate, just looking at it, and it is definitely going to be difficult to bat on over the last day."
The 36-year-old opening batsman moved past former national captain Allan Border to become the eighth all-time player with the most Test centuries.
The powerful left-hander continued his liking for India's bowlers, bringing up his fourth century against them to average 65.14 compared to his career average of 53.04.
"I've built this particular match up in my mind more than any other, it announces the summer, it's the vibe of the ground, the spirit of Christmas, having your families around, I just think it's one of those events that I really enjoy," Hayden said.
"I really enjoy playing spin bowling, and the majority of overs today were spin on a first-day wicket as well."
Hayden was finally out when he miscued to Rahul Dravid at mid-on off Zaheer Khan, a half hour after tea.