Schalke, who won the last of their seven titles in 1958 but have been runners-up three times since 2001, went ahead in first half stoppage time when 18-year-old Joel Matip headed in Lukas Schmitz's cross.
It was one of only a couple of goalscoring chances in a disappointing 45 minutes.
Peru striker Jefferson Farfan extended their lead in the 81st minute when he scored with a neat finish from close range after Kevin Kuranyi beat his marker down the right and crossed.
Cologne, who had three players sent off in a 2-0 German Cup defeat at Augsburg on Wednesday, rarely threatened the hosts.
"It was very difficult for us to create chances," said Schalke coach Felix Magath who last year led VfL Wolfsburg to the title.
Magath's team are third on 45 points. Leverkusen beat Wolfsburg 2-1 on Saturday while Bayern, second on goal difference, defeated Borussia Dortmund 3-1.
Freiburg, in 15th spot, lost 2-1 after a stoppage-time goal at seventh-placed Eintracht Frankfurt.
Papiss Cisse pounced on a goalkeeping blunder to put the visitors ahead in the 25th minute, only for Benjamin Koehler to level with a free kick 15 minutes later.
Eintracht dominated the second half and were rewarded when Halil Altintop struck with almost the last kick.
