The hosts were never really troubled by Labbadia's men, and take all three points to keep the pressure on the Bavarian giants at the league summit
Joel Matip scored the hosts’ fastest goal of the season after only three minutes, and second half strikes from Kyriakos Papadopoulos and Julian Draxler made the points safe, despite Shinji Okazaki's late consolation.
Schalke made a blistering start to the contest, and took the lead after only three minutes of play. Benedict Howedes rose highest from a corner to flick the ball into the path of Matip, who made no mistake from a few yards out.
Stuttgart was nowhere to be found as the home side continued to attack, and Chinedu Obasi had a shot saved by the legs of Sven Ulreich before Klaas-Jan Huntelaar saw an effort ruled out for offside after eight minutes.
After producing nothing of note for the opening half hour, Bruno Labbadia’s men belatedly registered their first chance when Lars Unnerstall was forced to parry an attempt from a tight angle by Cristian Molinaro.
However, despite failing to match the intensity of the opening 10 minutes, Schalke were always in control, and went close again in the 58th minute when Huntelaar latched onto Draxler’s through ball to force Ulreich to parry out for a corner.
The respite was only momentary however, as from Draxler’s resulting delivery, Papadopoulos rose highest to emphatically nod the hosts into a two goal lead.
Hubb Stevens' men kept up the pressure, and Huntelaar was foiled by Ulreich again from a one-on-one situation. However, Stuttgart almost found a way back into the game in the 72nd minute after a miscue by Papadopoulos, but for a goal line clearance by Christian Fuchs.
Schalke put the game to bed with 10 minutes remaining, after a lovely passing move involving Huntelaar, Raul and Draxler carved the visitors apart and allowed the young German to slot home past the hapless Ulreich.
The visitors pulled one back with three minutes to go after a scramble in the box left Okazaki with a relatively simple finish fron 12 yards out. However, the goal proved to be little more than consolation as the hosts ran out comfortable winners.
The result sees Schalke move up to second place in the standings, behind leader Bayern Munich only on goal difference. Stuttgart meanwhile sits in ninth place with 22 points.