Ravichandran Ashwin, Ravindra Jadeja and Axar Patel scored 177 runs in India's 400 in the first Test in Nagpur, while in Delhi they contributed 134 priceless runs out of a team total of 262.
He is the ninth bowler and fifth spinner to complete the feat in Tests.
Ravichandran Ashwin becomes leading wicket-taker in Border-Gavaskar Trophy history
Despite doing well in the IPL and domestic cricket over the past two seasons, Varun did not get a recall to the Indian team and that only made him hungrier.
Injured captain Michael Clarke has been named in Australia's 15-man squad for the World Cup in February and March.
India play three ODIs against Australia starting in Sydney on Saturday before travelling to New Zealand for a five-ODI and three-T20I assignment starting January 23.
The tourists were left on 20-2 after seven overs going into the second day.
India skipper Rohit Sharma chose to keep suspense over his preferred batting and bowling line-ups for the opening Test against Australia.
"I think patience will obviously be the key. The challenge will be to keep going if you get a start."
Cricket Australia on Tuesday confirmed former India One-Day International player Sriram Sridharan will join the coaching staff for the forthcoming Test tour of India as a spin consultant.
Australian captain Aaron Finch is confident Glenn Maxwell's ODI absence won't last long.
Part-time off-spinner Glenn Maxwell can see himself playing a bigger role behind specialist spinners Nathan Lyon and Adam Zampa.
It's been more than a decade since India lost a Test series at home - they had lost to England 1-2 in 2012.
Who do you think should be part of India's playing XI for the second Test against Australia in Adelaide?
Images from Day 5 of the first Ashes Test between England and Australia at Edgbaston Cricket Ground in Birmingham on Tuesday.
The two players were eligible for Aaron Finch's national side after their 12-month suspensions for ball-tampering ended last month.
Australia meet South Africa in a one-off T20 match on the Gold Coast on November 17, before three T20s against India starting in Brisbane on November 21.
Ashwin's legacy, marked by his intellect and dominance on the field, will resonate for years to come.
The biggest positives with the bat in Perth were Virat Kohli regaining his rhythm and Jaiswal's coming of age hundred in his debut Test in Australia. Both will look to build on those significant gains in Adelaide.
The absence of an attacking spin bowler in the Indian side is hurting the visiting team's chances.
Australia spinner Nathan Lyon fought hard to cement his place in the Test team and now hopes to convince selectors of his white ball prowess in time for the World Twenty20 in India.
Australia will play two spinners in the first Test against Sri Lanka at Pallekele on Tuesday, captain Steve Smith said, as the world's top-ranked side eye a turnaround in their poor record on the slow pitches in Asia.
Allan Border opened up on the team's selection and said Australia overthought during the first Test in Nagpur.
Australia's cricketers will just have to bear English taunts over the ball-tampering affair on tour next month for the one-day international series, spinner Nathan Lyon has said.
Australia's in-depth planning to subdue Cheteshwar Pujara worked out well in the opening Test but spinner Nathan Lyon says it would be a massive challenge to keep the world-class batsman quiet through the remainder of the series.
Any of these match ups could influence the outcome of the Perth Test.
One piles up runs, the other piles up wickets. Both Kane Williamson and Tim Southee will hope to add to their hauls when they play their 100th Test match against Australia in Christchurch this week.
Australia's opener Matt Renshaw tests positive for COVID-19, will feature in Sydney Test against South Africa
A resolute Ravichandran Ashwin and a hamstrung Hanuma Vihari battled pain and a hostile Australian bowling attack while displaying the largely extinct art of Test-saving batsmanship to snatch a remarkable draw for India in the third Test, after Rishabh Pant raised visions of an improbable victory, at the Sydney Cricket Ground, on Monday.
With the series locked at 1-1, Brisbane could well decide the course of the rubber and whether Rohit's men would continue to be the master of their fate in the ongoing World Test Championship.
Australia's assistant coach Daniel Vettori said he does not mind the spin-friendly pitches on offer in their series in India as they have challenged the batsmen and brought their skill and perseverance into play.
Australia captain Pat Cummins admitted his team had endured an uncomfortable time before winning the second Ashes Test against England at Lord's.
Australian batter Usman Khawaja believes the 50-over format needs to be reduced to 40-overs-a-side game to make it more interesting in the wake of ever-growing popularity of T20 cricket.
The absence of the dashing wicketkeeper-batter leaves a big void in India's Test eleven, said Hayden
England will not change their attacking philosophy in the second Ashes Test against Australia at Lord's this week.
Team Director Ravi Shastri has praised R Ashwin for his performance in Sri Lanka and called him the best off-spinner in world at the moment.
The visitors, who are 2-0 behind in the four-Test series for the Border-Gavaskar Trophy, finished the frenetic opening day 47 runs ahead with six wickets in hand.
'I think they're feeling the pressure a little bit to be honest'
Images from Day 1 of the fifth Test between Australia and India at the Sydney Cricket Ground on Friday.
Labuschagne said Australia were expecting a little more help from the fifth day pitch but credited India for hanging on for a remarkable draw.