Iyer made 117 off 142 balls with the help of 15 boundaries and two sixes to single-handedly take Mumbai to 262 for eight in 66 overs in reply to Saurashtra's 235 all out.
Besides Iyer, Surya Kumar Yadav (48) was the other notable scorer for Mumbai.
At stumps, Siddhesh Lad was batting on 22 while Iqbal Abdullah was unbeaten on 9.
Left-arm pace duo of Hardik Rathod (3/44) and Jaydev Unadkat (2/55) shared five wickets between them while right-arm fast bowler Chirag Jani (2/46) also chipped in with two wickets.
Debutant Prerak Mankad (66) added 11 more runs to his last night's score before becoming Dhawal Kulkarni's fifth victim of the innings.
Jaydev Unadkat also chipped in with a handy 31 off 26 balls during which he struck two boundaries and as many sixes.
Kulkarni (5/42) finished with an impressive five-wicket haul while Shardul Thakur scalped three wickets giving away 89 runs.
At the end of day two, Mumbai enjoy a slender 27 runs lead over Saurashtra with just two wickets in hand.
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