Dennis Geiger put the visitors ahead after good work from Kerem Demirbay and Nadiem Amiri after 10 minutes.
Wagner, battling for a spot in next year's World Cup squad, doubled the lead with a 56th-minute penalty and volleyed in Andrej Kramaric's cross at the far post 10 minutes from time.
Cologne failed to show any of the form that helped them crush BATE Borisov 5-2 in the Europa League in midweek and remain bottom with two points and no wins from 11 games.
Hertha Berlin's Davie Selke got a late equaliser to deny VfL Wolfsburg a first victory under coach Martin Schmidt, who now has a record-extending seven straight draws since taking over.
The Wolves missed a penalty and had two efforts disallowed after advice from the video assistant referee in the first half but still led 3-2 before Selke got a lucky bounce to tap in the leveller in the 84th minute of a topsy-turvy encounter.
Wolfsburg are 14th on 11 points with Hertha in 11th, three points ahead.
Champions Bayern Munich opened up a four-point lead at the top with a 3-1 victory at title rivals Borussia Dortmund on Saturday. Bayern have 26 points with RB Leipzig, 2-1 winners at home to Hanover 96, in second on 22.
Third-placed Dortmund are on 20, level with Schalke 04, and Hoffenheim are fifth a further point behind.
(Reporting by Karolos Grohmann, editing by Ed Osmond and Ken Ferris)
