At stumps, Mumbai were 495 for 6 in 112 overs, replying to Punjab's measly 154, with Tare (111) and Dhawal Kulkarni (30) at the crease, with two days left in the Group B game.
Iyer made runs at a breakneck speed to continue from his yesterday's score of 61 to slam the fourth fastest double century by an Indian batsman in first class cricket.
Iyer reached the coveted figures off just 175 balls with the help of 25 fours and five sixes.
The 20-year-old player, who carted the clueless Punjab attack to all parts of the field and showed superb timing in his strokes, fell for 200 off the next ball he faced after reaching the landmark with a single.
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Iyer, who batted for 292 minutes in scoring his third first class ton, was dismissed in trying to clear the rope for the sixth time in his innings by his Delhi Daredevils teammate and Punjab captain Yuvraj Singh.
Later, he and his captain Tare, who has faced 140 balls and struck 15 fours, combined to add 64 runs for the fourth wicket to completely demoralise the Punjab attack in which left-arm pacer Barinder Singh Sran was the lone bright spot with a three-wicket haul.
Though Mumbai lost the wickets of Sidhesh Lad and Abhishek Nayar cheaply, Tare - who reached his sixth first class ton in 128 balls - and Kulkarni kept the Punjab fielders chasing leather with a stand of 71 runs for the seventh wicket.
Punjab: 154
Mumbai 495 for 6 (S Iyer 200, S Yadav 78, A Tare 111 not out, D Kulkarni 30 not out; Barinder Singh Sran 3/87).