Werder Bremen moved up to third when Brazilian defender Naldo gave them a 3-2 win at Hertha Berlin in the day's other game.
Guerrero took his tally to four goals in as many games as Hamburg edged ahead of Bayer Leverkusen on goal difference, both sides having taken 10 points from their opening four games.
The Peruvian opened his account in the 19th minute, scoring with a left-footed shot into the bottom corner after David Jarolim pounced on a mistake by Cologne's Pierre Wome.
In the 66th minute, he doubled Hamburg's lead with a shot which deflected off Youssef Mohamad.
Sunday's other match produced five goals in the final 35 minutes.
Mesut Ozil put Werder ahead in the 57th minute and Tim Borowski made it 2-0 by slotting home Marko Marin's pass in the 74th.
