At the end of the initial 10-over powerplay, India were 41 without loss after captain Virat Kohli won the toss and batted -- a decision he said was a "no-brainer" given the conditions at the Oval.
Left-hander Dhawan was the more fluent of the first-wicket duo, his unbeaten 27 including four boundaries.
By contrast Sharma, 11 not out, survived some early jitters and a half-chance dropped at short midwicket by Nathan Coulter-Nile off Mitchell Starc.
Reigning champions Australia's new-ball duo of Pat Cummins and Starc both bowled a probing line to test the Indian openers with pace and swing on a sunny morning in south London.
Dhawan broke the shackles with three boundaries in Coulter-Nile's first over -- shots greeted with huge cheers from a largely India-supporting crowd.
Both teams are looking to stay unbeaten in the 50-over showpiece event with Australia winning their first two games and India defeating South Africa in their first match of the tournament.
The top four sides from the 10-team round-robin group stage will contest the semi-finals, with the final at Lord's, in northwest London, on July 14.