The left-hander struck two big sixes and seven fours in his 142-minute at the crease to bring back memories of his last visit to India when he scored more than 500 runs in the three Test-series.
His authoritative knock helped Australia, who elected to bat, to end the day at 159 for the loss of three wickets.
At stumps, right-handers Damien Martyn and Brad Hodge were at the crease with Martyn looking particularly impressive in making a composed 28 in 70 minutes. Hodge was on 6 after 18 minutes of stay.
Hayden was deceived by Mumbai captain Sairaj Bahutule, who caught and bowled the Australian opener in the post tea session. Others to be dismissed were Hayden's opening partner Justin Langer (24) and another left-hander Simon Katich (30).
Only 210-minute of play was possible after the entire morning session was abandoned because of damp conditions following heavy thundershowers that lashed the metropolis last night and this morning.
But once play commenced at 1:40 pm, after a delay of three and a half hours, the Australian openers began on a brisk note. Hayden pulled, swept, drove and cut his way to his half-century off only 61 balls.