First-half goals from Miguel de las Cuevas and Andre Castro decided the game in favour of Sporting, who move two points clear of the bottom three with the victory.
Sporting finished the match with 10 men following the 85th-minute dismissal of Alberto Lora, but there was still no way back for Getafe, who now find themselves only seven points above the drop zone after another disappointing result.
Michel's men had ended 2010 looking set to make a bid for the European places, but 2011 has brought them just one win in 11 league matches and things could get worse as their next three outings are against top-six sides Athletic Bilbao, Barcelona and Valencia.
Sporting were quickly on top at El Molinon and almost took the lead inside the opening two minutes when Nacho Cases drilled a 30-yard strike against the crossbar.
Ivan Hernandez then drew a finger-tip save out of Getafe goalkeeper Jordi Codina before the hosts opened the scoring in the 32nd minute through De las Cuevas, who twisted and turned on the edge of the area before firing a low shot through a group of players and past a helpless Codina.
Sporting made it 2-0 nine minutes later when Castro picked up a pass 30 yards out before drilling a low shot past Codina.
The home side twice came close to making it 3-0 either side of half-time, with David Barral firing just wide of the far post from an acute angle after going past Codina, before the same player dinked a chip over the stranded Codina, but also over the bar.
Getafe should have pulled a goal back in the 59th minute when Adrian Colunga got in behind the Sporting defence, but he dragged his shot wide with just Ivan Cuellar to beat.
Javier Arizmendi then fired an ambitious effort over for the visitors before Sporting struck the woodwork again in the 74th minute.
The unmarked Andre Castro must have felt he had netted his second of the match when he powered a header goalwards from six yards out, but Codina stuck up a hand and managed to divert it onto the bar before gratefully grabbing the rebound.
Sporting had to play out the final five minutes with a man less after Lora was shown a yellow card after an attempted cross had struck his arm, but it made no difference to the final outcome as Manuel Preciado's men escaped the relegation places.