Former cricketers lauded Australia and India for a hard fought first Test, which the hosts won by 48 runs after a spectacular batting collapse saw the visitors lose eight wickets for 110 runs in the final session of the match.
India started the fifth and final day requiring 364 runs to win after Australia declared on their overnight score of 290 for five.
Skipper Virat Kohli (141) and Murali Vijay (99) had looked to put India in the driving seat with the score on 205 for two at tea and the visitors needing 159 runs off 37 overs in the final session.
Nathan Lyon's brilliant spell of off-spin bowling saw India lose eight wickets to be bowled out for 315 and fall well short of the target. The Australian bowler was the catalyst picking up seven wickets for 152 runs to give his team a 1-0 lead.
Former Australian pacer Glenn McGrath congratulated the team and tweeted that a chance of beating India 4-0 was still alive.
"Sensational win by the Aussies. Hung in there all day & got their rewards. Well played boys. 4 nil still alive!! #AUSvIND," tweeted McGrath.
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McGrath, also called 'pigeon' by his teammates praised Indian captain Kohli for back-to-back centuries.
"Great innings by @imVkohli Second hundred for the match. Fought all the way. Well played mate."
Indian spinning great Anil Kumble rued India's collapse, tweeting,: "Well done Aus.Remarkable win. @NathLyon421 well bowled! Ind fell apart in a session. Worrying nobody showed fight after V & V (Virat and Vijay)."
South African Jonty Rhodes wrote: "Sad I missed end of #AUSvIND sounded like good cricket all round."
Former India spinner Bishan SIngh Bedi chose to look at things more positively and said he was looking ahead to the remaining three Tests.
"Ind lose but are far frm disgraced.Alas ViratK was left stranded..nobody wins if team loses!Now gud tempo's set fr remaining 3 Tests..!!."
Former Australian batsman Dean Jones was all praise for the cricket on offer and praised both the teams for an excellent showing.
"This match proves again that Test Match cricket is the greatest game of all! Well played India & Aust and awesome performance from Lyon!"
Australian leg-spinner Stuart MacGill congratulated Lyon, who took five wickets in the first innings ended the match with his first career 10-for.
"well played @NathLyon421 enjoyed every single ball you bowled. world class."
"All over @CricketAus win first test. @NathLyon421 #MOM what a brilliant test match!," tweeted Tom Moody.
Meanwhile, former Aussie pacer Damien Fleming chose to remember fallen compatriot Phillip Hughes while fast bowler Pat Cummmins dubbed the win special.
"Aussies win and they run straight 408 number painted on outfield," tweeted Fleming.
"Special, special win!!!," said Cummins.
Former Indian batsman VVS Laxman praised India for their positive approach and for not settling for a draw.
"Test cricket at its best. Congrats Aus. Also pleased to see the positive approach of Ind. They were always looking to win," tweeted the stylish batsman.