Smith continued to steady the attack, but ended his innings just shy of a half-century after he was dismissed for an lbw on 47 following a Karn Sharma delivery.
Warner impressed for Hyderabad in their reply by racking up 12 boundaries and three sixes in his stint at the crease, which ended on 90 runs when he was bowled out by John Hastings.
Hyderabad were in a strong position on 116 runs for the loss of just one wicket, but Chennai eventually found the breakthrough by taking out Naman Ojha (19).
Shikhar Dhawan continued to frustrate the bowlers by reaching 64 runs with the help of four boundaries and two sixes in Ranchi.
Despite losing another two wickets, Hyderabad were able to hold out to clinch the victory on 189-4.