Saurabh scored 109 while the other contributions came from Daryl Ferrario (55), Siddharth Akre (54) and opener Abhishek Goswami (58), taking India to 388 for nine declared in response to England's 375 all out in the first innings.
England had lost their openers in the second innings and were 34 for two in nine over at close of play.
India, resuming the day at 153 for three, ended up surpassing the visitors' total.