Sharma enjoyed big partnerships of 125 with Virat Kohli (59) and 121 with Ajinkya Rahane (89) as the Indians punished a below-par Australian attack.
Although the score was the biggest by an international team in ODIs at the Gabba, the Indians looked headed for a much bigger total until they lost a clatter of wickets in the final few overs.
Sharma, who led from the front once again, appeared to edge a ball from left arm quick Joel Paris to wicketkeeper Matthew Wade when he was on 89.
But he took full advantage of his reprieve from umpire Mick Martell to smash 124 runs from 127 balls, adding to the magnificent 171 not out he scored in the first ODI in Perth on Tuesday.
Sharma hit 11 fours and three sixes on his way to his 10th ODI century.
After losing his opening partner Shikhar Dhawan for just six, Sharma was joined at the crease by Kohli and the pair took up where they left off in Perth by dominating the Australian attack.
Both reached 50s with little trouble, mixing quick singles and well-run twos with punishing boundaries.
But with the score on 134 Kohli pulled Scott Boland to fine leg and was run out by a superb Kane Richardson throw while attempting a risky second run.
The busy Rahane joined Sharma and kept the score moving, cruising to a run-a-ball 50 before he drove a James Faulkner slower ball into the pitch and the bowler deflected the ball on to the stumps at the non-striker's end, leaving Sharma stranded.
At 255-3 with almost eight overs remaining India would have been hoping to reach at least 320.
However, Australia took some quick wickets to slow the scoring and will be confident of chasing down the total to go ahead two-nil in the five-match series.