Finn is among an ever-decreasing number of players who have played more Tests than ODIs. He has taken 50 wickets in 12 Tests but only seven from six ODIs
When Jonathan Trott was bowled by a Naidu delivery that kept low and Ian Bell fell to Ashish Reddy's first ball England were 47-4 in the 14th over and struggling.
Bopara, though, led the counter attack with a six off Amol Shinde and he received fleeting support from Jonny Bairstow (15) and Samit Patel (20).
But when the Essex player was seventh man out, England still had only 169 on the board and but for Chris Woakes' unbeaten 46 would have been set for a total short of 200.
Woakes, who came in at number eight, said: "It's nice to bat higher up the order if you can, but anywhere I can slot into this team will be good. My batting is something I've worked on really hard."
Even 219 looked like it would be far from satisfactory when Akshat Reddy hooked Finn's first ball over the rope but he only added one more to his score before being run out as Hyderabad lost wickets at regular intervals.
Arjun Yadav held the innings together with a patient 47 but when Woakes clean bowled two batsmen with successive balls the home side were 99-5.
And although they staged a rally of sorts, Finn returned to mop up the tail in stunning fashion.
The 22-year-old had Shinde caught behind by Bairstow before bowling Kaneshuk Naidu and seeing Ahmed trapped in front of the stumps.
tweeted: "To get a hat-trick was awesome, first time I've ever done it."
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