The win for Sevilla sees Michel's side move up into eighth place and keeps them in the hunt for a European qualifying spot.
Alvaro Negredo, Manu and Jesus Navas were on target for the hosts in the second half, while Tomer Hemed grabbed a late consolation for Mallorca, who remain in 13th place after defeat.
It was Navas who went closest to opening the scoring early on, the Spain international bringing a fine save out of Dudu Aouate in the Mallorca goal.
Aouate then saved again from Manu and Jose Antonio Reyes before Navas, Piotr Trochowski and Andujar Coke all shot off target.
The deadlock was finally broken on 51 minutes when Negredo got his head to a Reyes corner and 10 minutes later the hosts' lead was doubled by Manu who fired low past Aouate.
Victory was made certain by Navas in the 68th minute and despite Hemed's excellent effort on 74, Sevilla coasted to the final whistle and all three points.