Leverkusen's win came as Niko Kovac claimed his first victory as Borussia Dortmund coach on Saturday in a 6-0 thrashing of Union Berlin, which featured a four-goal salvo from Serhou Guirassy.
Title holders Leverkusen have now closed the gap to leaders Bayern Munich to five points - temporarily, at least, before Bayern, who are their opponents in the Champions League last-16, have the chance to restore their eight-point advantage when they host third-placed Eintracht Frankfurt on Sunday.
Elsewhere in Saturday's programme, VfL Wolfsburg fought back for a 1-1 draw with lowly Bochum, in-form Mainz defeated promoted St Pauli Hamburg 2-0, and Alexis Claude-Maurice scored a hat-trick in Augsburg's 3-0 win against 10-man Borussia Monchengladbach.
Leverkusen were dominant, taking an early lead in the ninth minute through Patrik Schick, who volleyed Amine Adli's cross into an empty net.
Adli then got a goal himself as he took a perfect-timed pass from Florian Wirtz and chipped it over the goalkeeper from close range in the 45th.
"We controlled the game well and dominated it, even though it wasn't easy. Patrik's first goal was important to win this game. After the last two away draws, today's win was even more important for us," coach Xabi Alonso said.
Following two consecutive defeats in the Bundesliga, Dortmund finally tasted victory again - and in style in front of their passionate fans.
Diogo Leite's own goal in the 25th minute put them in charge, before Pascal Gross, who hit the crossbar on the half-hour, then served Guirassy, who nodded the ball home from close range in the 40th.
That marked the start of a gala evening for Guirassy, who added a second-half hat-trick.
He was again assisted by Gross to add a second to his name in the 75th before completing a hat-trick in the 80th and heading in one last effort three minutes later.
Maximilian Beier in the 89th made it six in what was only Dortmund's second league win this year and a first for coach Kovac, who took over at the start of the month after the dismissal of Nuri Sahin.
Dortmund moved up one position to 10th and are seven points from the Champions League spots.
Another striker in fine form was Claude -Maurice, who made Gladbach pay after they'd gone down to 10 men in the 28th minute following goalkeeper Jonas Omlin's red card for fouling Phillip Tietz outside the box when he had a clear goalscoring opportunity.
Midfielder Claude-Maurice then scored Augsburg's opener in the 55th minute, and added a second in the 61st with a low shot from the edge of the area before crowning his big afternoon by completing his hat-trick nine minutes later.
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