The run of results moved Werder up to eighth place on 26 points, well clear of the danger zone where Borussia Dortmund (on 19 points), Freiburg and Vfb Stuttgart (both on 18 points) are battling for survival.
Former German champions Werder took the lead in the 17th minute with a goal out of nowhere when Davie Selke, the talented 20-year-old Germany youth international, connected directly with a deep Fin Bartels cross.
Zlatko Junuzovic then curled a free kick in from 18 metres just before the half-hour mark as Leverkusen struggled to find their rhythm.
The visitors, who are sixth on 32, recovered towards the end of the first half, cutting the deficit with a Hakan Calhanoglu rebound header before taking control of the game.
But despite a largely one-sided second period with Leverkusen pushing for the equaliser, they failed to score although they did hit the post through Stefan Kiessling before coach Roger Schmidt was sent to the stands for dissent.
Leaders Bayern Munich beat VfB Stuttgart 2-0 on Saturday without hitting top form to stay eight points clear of second-placed VfL Wolfsburg, who beat Hoffenheim 3-0 to move up to 41.
In the other game on Sunday surprise package Augsburg missed a huge opportunity to go third when they squandered a 2-0 lead against Eintracht Frankfurt to draw 2-2.
Augsburg, more used to battling relegation than playing for a Champions League spot, looked set to continue their stellar run this season when they caught their opponents twice off guard for a 2-0 lead in the first half.
Estonia international Ragnar Klavan slotted in from seven metres and Raul Bobadilla doubled the hosts lead at the far post in the 37th after Tobias Werner twice floated free kicks into the box which defenders failed to clear properly.
The visitors pulled one back on the stroke of halftime through Stefan Aigner after a scramble in the box to reignite their hopes.
With Augsburg losing much of their pace in the second half, Bundesliga top scorer Alex Meier hit on the break, drawing them level when he raced clear to slot in for his 14th goal of the campaign in the 70th.
Augsburg remain in fourth place, level on 34 points with third-placed Schalke 04 with Frankfurt ninth on 25.
(Reporting by Karolos Grohmann, editing by Pritha Sarkar)
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