Michel's men, looking to earn a place in Europe next season, find themselves five points off the fourth place in La Liga after a convincing victory
With a wet pitch making possession and movement difficult, a scoreless first-half had both teams feeling confident of earning a victory, but brilliant finishes by the hosts put things out of reach of Mallorca.
Sevilla, who boosted their chances of European football with the win, managed to earn their third straight league victory, all of which saw them score three goals.
In the first half, things got going after 15 minutes as the hosts created their first solid chances, with Jesus Navas making the most noise.
The Spain international nearly found the target with two efforts from inside the box on the right, with his first attempt being blocked by a defender before pouncing on the rebound, firing a shot that was made difficult thanks to Dudu Aouate, who managed to get a hand on the ball to send it wide.
Moments later, Navas made a quick run down the right before lifting a soft effort to the middle of the box, where Manuel del Moral got a head on it but knocked the ball high and wide.
In the subsequent minutes, the home team managed to continue to threaten but nothing came of it as the teams entered the break just as they had started.
In the second half, it took only five minutes for the opener.
Off a corner and with numerous players at the front post, Alvaro Negredo managed to flick on a cross from Jose Antonio Reyes with his head, finding the far side of the goal, sending the Sevilla faithful into an uproar.
Just over 10 minutes later, the hosts doubled up their opponenets thanks to Del Moral, who was sent through into the left side of the box with a smooth pass from Navas, before finishing at the right side with a soft shot that hit the post before going in.
The fans only had to wait five more minutes for the third goal as Sevilla put the match out of reach. Navas started the attack with a ball to the left wing to Reyes.
The former Arsenal man proceeded to play a perfect, low ball to the far post to split several defenders and find Navas, who finished with little trouble past the Mallorca custodian.
The visitors managed to get one back after Tomer Hemed put away a cross from Pablo Caceres at the near post 17 minutes from time, but the dramatic comeback did not come to fruition as Sevilla earned the quality victory by containing the Mallorca attack for the rest of the match.
The Islanders, who remain on 36 points and are in 13th place, host Granada next weekend. The home side, who are in eighth with 42 points, travel north to take on Athletic Bilbao.