Venugopal smashed a century but got little support from teammates as Gujarat scored 277/7.
While Rao had gathered 75, Bhatt was steady on 34 when play ended for the day.
Hyderabad have lost both their opening games in IPL 2014.
Parthiv Patel was well supported by Venugopal Rao, who made a 27-ball 47.
Gujarat chased down the target in the penultimate ball of the match in the Vijay Hazare tournament.
Gujarat placed themselves in a strong position as they first took a 99-run first innings lead.
Venugopal Rao scored a century as Gujarat declared at 479 for eight.
Parthiv Patel cracked his 21st first-class century to power Gujarat to 287 for three.
Bhargav Merai struck a fine century to take Gujarat to a respectable 314 for four.
Gujarat skipper Parthiv Patel missed out on a double century but the visitors managed to secure a 63-run first innings lead over Jharkhand on the third and penultimate day of their Group A Ranji Trophy match.