Both goalkeepers had comfortably dealt with long-range efforts all afternoon as neither side looked capable of breaking the opposition down until the Levante substitute latched onto a loose ball just inside the Getafe half and took a touch before looping his effort over the helpless Miguel Angel Moya.
A second consecutive 1-0 win for Juan Ignacio Martinez's men moves them up into fifth, whilst Getafe slip back into the bottom half.
The visitors had started the game brightly as Jose Barkero forced Moya into the best save of the opening period with a powerful strike from 25 yards that the keeper did well to claw away, but the game soon descended into a scrappy affair with both sides failing to hold onto possession for any period of time.
Getafe did begin to improve just before the break as Jaime Gavilan forced Gustavo Munua to turn away his effort from a narrow angle before Rafa Lopez ought to have scored as he beat Munua to Pedro Leon's corner but the defender's header flew over the bar.
The introduction of Diego Castro, who had been surprisingly left out by Luis Garcia after scoring the winner in each of Getafe's past two outings, gave the hosts an extra impetus on the hour mark and Munua had to be alert to parry another two efforts from distance by Leon and Mehdi Lacen before the Uruguayan easily pounced on Alvaro Vasquez's weak header.
But it was the visitors who eventually made the breakthrough on 87 minutes as Michel smashed in his fourth goal of the season to ensure a first away win of the season for Levante.