Warner, 25, raced to 104 not out as the hosts piled on 149-0 after bowling India out for only 161.
It was the fastest Test century by an opener - only 69 balls - and he brought it up with a huge six over long on.
India lost their last six wickets for 30 runs, with pacemen Ben Hilfenhaus taking 4-43 and Peter Siddle 3-42.
Warner, who played county cricket for Durham in 2009, said: "It's a pretty good feeling. The ball moved about but I just played my game.
"I've been lacking self-confidence but I showed the aggression I normally play with.
"In my mind I think India are bowled over already. I hope we can get this Test out of the way, capitalise on the start we've got and win this Test first.
"We're 2-0 up in the series, hopefully we can put 400-500 runs on the board and bowl them out again.
"If we can take the series that will be fantastic. Time will tell if we win 4-0 or 3-0."
Ed Cowan was unbeaten on 40 alongside Warner and Australia, who lead the four-match series 2-0, are on target for a victory which would hand them the series.
Australia's all-pace attack gave them the platform to work from by ripping into the Indian top order after winning the toss.
Hilfenhaus removed Virender Sehwag and Gautam Gambhir in the morning session.
Siddle accounted for Rahul Dravid, bowled for the fourth time in five innings, while Ryan Harris, in his first Test appearance since November, disposed of Sachin Tendulkar.
Virat Kohli and VVS Laxman provided some resistance but once they subsided India fell apart.
Warner came in not long after tea and got straight to work, shrugging off a blow to the side of the head from paceman Umesh Yadav.
He changed his helmet and then rattled the next two balls to the boundary on the way to his magnificent century.
"I was a bit shaken up, but that's cricket," Warner said. "You have to watch the ball and I didn't."

Sum: David Warner scored the equal fourth fastest century in Test history as Australia took control on day one of the third Test against India in Perth.


Ciaran Williamson, eight, was playing with friends in Craigton Cemetery when a headstone fell on him on 26 May 2015.
Alastair Brown later told the HSE that the council had a "formal process of inspection" for cemeteries before 2015.
A QC for Ciaran's mother stated that no evidence existed for this claim and accused him of misleading inspectors.
Mr Brown, who was head of environment and sustainability at Glasgow City Council from 2008 until September 2016, was giving evidence for a second day at the fatal accident inquiry into Ciaran's death.
The inquiry, at Glasgow Sheriff Court, aims is to establish if there were any reasonable precautions that could have prevented the tragedy.
It also aims establish if there were any defects in the system of work which caused or contributed to Ciaran's death.
The inquiry heard that Mr Brown wrote to the health and safety executive following the tragedy.
In his letter, he said the council had established a "formal process of inspection" before 2015.
The letter also said: "Whilst there does not seem to be any formal inspections undertaken from 2011 there are reports of a number of inspections on an ad hoc basis."
Paperwork sent to the HSE included 11 reports of checks at cemeteries in Glasgow, between 2006 and 2011.
Six cemeteries had only one report while two others had multiple checks over those years.
An example of one record from Sandymount cemetery, dated back to 2006 and recorded three memorials being checked.
Dorothy Bain QC representing Ciaran's mother, Stephanie Griffin, questioned Mr Brown about the records.
She said: "There's no record for Craigton here."
The witness replied: "There's no record for Craigton.
Ms Bain put to him: "The records - clearly meaningless, aren't they?"
Mr Brown said he "wasn't familiar with guidance" but said he would have thought they would have asked for "more explicit records".
Ms Bain continued "If this is all there is, there is no evidence whatsoever of what you have told the inspectorate, namely a formal process for the inspection of memorials within burial grounds.
"It's completely misleading the inspectorate."
The witness replied: "I would have expected the inspectorate if they were unhappy with phraseology to come back to me for more records."
Mr Brown said that from 2003 onwards it was a "fairly unplanned activity".
The inquiry before sheriff Linda Ruxton continues.

Sum: A former council official has been accused of misleading the health and safety executive (HSE) after a child died at a cemetery in Glasgow.


Jordan Watson's body was found in the graveyard in Carlisle early on Tuesday morning; Cumbria Police initially said a man had been killed.
A post-mortem examination revealed he died from multiple wounds to the head and neck caused by a sharp implement.
Detectives said they were shocked by the murder and said for a child to die in such circumstances was "appalling".
The body was found in Upperby Cemetery, next to St John The Baptist Church in Manor Road, at about 07:45 BST on Tuesday.
Police patrols have been increased across the Carlisle area while the investigation continues into the death of Jordan, who lived in Ridley Road in the city.
Det Supt Andrew Slattery said: "Jordan has lost his life as a result of a savage and brutal attack which has shocked the officers working on the case.
"For a child to die in these circumstances in Carlisle is appalling.
"The offender or offenders must be apprehended and I appeal to any members of the public with information to come forward.
"If anybody heard or saw anything unusual in the area of the cemetery on Manor Road overnight, I would urge them to report it to our incident room."
The Reverend Jim Hyslop, vicar of St John The Baptist Church, said the first he knew of Jordan's death was when he saw police vehicles outside his house opposite the cemetery.
He said: "Nothing like this has ever happened in the 20 years I have been at the church.
"Jordan's body was found in the older part of the cemetery, which has been here since the church was founded in 1840.
"We haven't been told too much and I've not spoken to many people about what has happened. My thoughts are with his family at this time."
Carlisle's mayor, Steven Layden, said the entire city had been left "shocked and appalled" by the murder.
He said: "This is outside the normal life of people in Carlisle. It's absolutely shocking and the savagery and brutality of this murder makes it doubly appalling.
"It is utterly, utterly shocking that a 14-year-old can die in such a way."

Sum: A 14-year-old boy found dead in a cemetery was the victim of a "savage and brutal attack", police have said.


The 25-year-old, who has played for Gloucestershire since 2010, has agreed a three-year contract with Middlesex.
"We have been looking to sign a fast bowler with white-ball pedigree," said Middlesex managing director of cricket Angus Fraser.
"In James I believe we have found a bowler that will add extra bite and quality to this area."
Fuller was a key part of Gloucestershire's winning One-Day Cup campaign this year, taking 15 wickets including 2-34 in the final at Lord's.
Born in Cape Town, South Africa, he holds a UK passport and has taken 101 first-class wickets at an average of 33.90 with best figures of 6-24.
He also has 58 List A one-day wickets at an average of 25.17 and 62 Twenty20 wickets in 46 games.
"I have watched James bowl on numerous occasions and have been impressed with what I have seen," added Fraser.
"He is a fine athlete with a strong, easy action that allows him to bowl with good pace. James is extremely ambitious and is the sort of character that fits what Middlesex are looking for."

Sum:
Middlesex have signed James Fuller after the fast bowler turned down a new deal with Gloucestershire.