Crotone remained bottom of the league with just one point — from a 1-1 draw against Juventus.
Atalanta came into the match on the back of two straight defeats in Serie A but looking to build off its comeback draw with Ajax in the Champions League, as well as hoping to boost its confidence ahead of hosting Liverpool on Tuesday.
Muriel had two good opportunities before he put Atalanta ahead in the 26th minute, gathering a ball from Ruslan Malinovskiy with his back to goal and spinning to drill it into the bottom corner.
The Colombia forward forced Crotone goalkeeper Alex Cordaz into another good save before doubling his tally in the 38th after being set up by Remo Freuler.
Crotone pulled one back just two minutes later when Simy beat Marco Sportiello from a tight angle.
Atalanta’s Duván Zapata, who has scored four goals in his last three matches, had two late chances but sent both narrowly wide.
INTER MISSES LUKAKU
Inter’s dependence on Romelu Lukaku was again illustrated as it struggled in the absence of its key forward.