Stefan Reinartz, with a header, and Stefan Kiessling, with his second goal of the game, scored in the last 10 minutes to finish off Stuttgart who had twice battled back from behind.
"After our (midweek Europa League) game in Kharkiv where it was freezing we had problems finding our game today," said Leverkusen coach Jupp Heynckes.
"But our difference today was we had choices on the bench, a luxury I did not have last season," he said, hinting at Michael Ballack's contribution after he came on in the 65th minute.
Champions League competitors Schalke 04 suffered a surprise 2-1 defeat at the hands of last-placed Borussia Moenchengladbach, who notched their first home win of the season on coach Lucien Favre's debut to move level on 19 points with Stuttgart.
Peer Kluge gave the visitors a second-minute lead but Gladbach, who looked transformed under Swiss Favre, levelled with Marco Reus before Cameroonian Mohamadou Idrissou, out of favour until recently, headed in the winner in the 23rd minute to leave Schalke languishing in mid-table.
Leaders Borussia Dortmund are 10 points clear after easing past St Pauli 2-0 on Saturday with second-placed Leverkusen on 45 points.
Champions Bayern Munich, who had briefly climbed to second following their 3-1 victory at Mainz 05 on Saturday, dropped back to third on 42.
KIESSLING BRACE
Leverkusen grabbed an early lead with Kiessling before Martin Harnik levelled in the 16th minute.
The hosts regained control of the game just before halftime when Stuttgart's shaky defence, which has let them down so often this season, left Gonzalo Castro unmarked to head in after goalkeeper Sven Ulreich had initially saved his shot.
Serb Zdravko Kuzmanovic came to the rescue firing in an unstoppable shot from 25 metres seven minutes after the restart to equalise yet again for the visitors, who also rattled the woodwork with Cacau just past the hour.
Another lapse in concentration allowed Reinartz to rise above Stuttgart defenders and head Leverkusen back into the lead in the 81st minute before Kiessling made sure of all three points after a fine effort from Sidney Sam.
