Kazakhstan, a rising force in amateur boxing who will host next year's World Championships, had pocketed a bronze elsewhere in the men's draw but when Sapiyev bounded into the ring, it looked like he was fully intent on getting gold.
The world championship silver medallist was much the quicker boxer in the opening exchanges, using his longer reach to keep Evans at bay with a right jab and scoring when he got in close with some right hooks.
Evans, who had been improving with every round, beating Ukraine's world champion Taras Shelestyuk in the semi-finals, looked shocked as the Kazak easily took the second round to open up a 10-5 lead going into the last.
Any slim chance Evans stood of adding to Britain's bumper Olympic gold haul evaporated when the busy Sapiyev landed all the powerful shots in the final round, one of them knocking Evans' gumshield out of his mouth.
After three rounds of absolute domination, Sapiyev threw his hands in the air and screamed as he returned to his corner and left the arena draped in the baby blue Kazakh flag.
Sapiyev's team mate Adilbek Niyazymbetov can add a second gold when he fights in the light-heavyweight final later on Sunday while super-heavyweight Anthony Joshua still has the chance of handing Britain a third gold.
Losing semi-finalists Taras Shelestyuk of Ukraine and Andrey Zamkovoy of Russia took bronze.