This figure broke a record after Hyderabad bought Pat Cummins for $2.5 million in the same auction and later made him captain.
Venkatesh Iyer remained unbeaten on 51 and captain Shreyas Iyer remained unbeaten on 58 and Kolkata achieved the target with 38 balls remaining.
Hyderabad will have another chance to make the final when they take on the winner of the eliminator in the second qualifier in Chennai on Friday.
“We have all played enough cricket and moving to a new place (Chennai) also helps us, so we have to put it behind us and move on,” Cummins said.
Ahmedabad remained hot as the afternoon temperature reached above 44 °C (111 °F) for the second consecutive day.
Many seats in the 132,000-capacity stadium were empty. Stadium officials said more than 75,000 fans brought water bottles to stay hydrated while braving the heat.
Bowlers also regularly took drinks on the outfield between overs.
Most of India's northern states have been under a government heatwave alert since last week, with the capital New Delhi recording temperatures of 47.4 degrees Celsius.