Ravi Bopara and Jonathan Trott scored half centuries to save England from total humiliation after captain Andrew Strauss' decision to bat backfired spectacularly as Peterson dismissed both openers in the first over.
Peterson also got rid of Ian Bell with a full-length diving catch off his own bowling for a spell of three wickets for three runs in 16 balls.
Trott eked his way to 52 in a 99-run, fourth-wicket stand with Bopara, who justified his selection ahead of Paul Collingwood with 60 at Chennai's Chidambaram Stadium.
Tahir took 4-38.