Curry and Poole scored 27 points each and Klay dropped 26 points while Nikola Jokic finished with 37 points and 18 rebounds.
Poole shines against the Heat, helping the Warriors snap a three-game losing streak.
Warriors were without Stephen Curry, Klay Thompson, Draymond Green and Andrew Wiggins on the second night of a back-to-back.
Jordan Poole scored 20 points and Jonathan Kuminga had 19 points for the Warriors, who lost for the fifth time in seven games.