The 27-year-old Dhawan smashed his way to an unbeaten 106 off a mere 90 balls as India went to tea at a commanding 156 for no loss, after Mitchell Starc dominated the third day's first session.
The Delhi batsman surpassed the record of earlier fastest hundred on debut which was in the name of West Indian Dwayne Smith who reached his century in 93 balls in the third Test against South Africa in Cape Town in January 2004.
Murali Vijay played his part in the first-wicket big century partnership, contributing an unbeaten 42 off 85 balls with the help of four fours and two sixes.
Interestingly, Dhawan raced into the 90s without hitting a single ball in the air. What makes his effort even more praiseworthy is that he maintained a strike-rate of over hundred almost all through his innings. It was a staggering 117.64 when Dhawan got to the three-figure mark.
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Ray Lindwall had scored exactly 100 against England at the MCG in 1947 while coming out at number nine.
Though he missed out on the hundred by a whisker, Starc, along with Steven Smith (92), frustrated the Indians for a while, helping Australia add 135 runs in the first session of play before Ravichandran Ashwin trapped last-man Xavier Doherty.
The Indians made three runs in the one over they played before lunch, with Vijay scoring all of them.