Mario Gotze opened the scoring midway through the first half with a tap-in at the far post, before an own goal from Daniel Halfar sealed the win for the champions in the 66th minute.
It was Guardiola's 50th victory since taking the helm at the Allianz Arena and his side's first on the road this season during an unbeaten start to their Bundesliga title defence.
And the former Barcelona coach could not hide his delight, telling the club's official website after the game: "We are very pleased that we have celebrated the first away win of the season.
"It was not easy, because Cologne was well organised. But we controlled the ball well and never lost concentration."
The win sees Bayern maintain their place at the top of the table and comes ahead of a UEFA Champions League trip to Moscow to face CSKA on Tuesday.
Guardiola had previously claimed the congested fixture list was "killing" even the most elite players, and revealed his side will not have chance to return to Bavaria before the trip to Russia.
The Spaniard added: "Now we sleep here in Cologne and tomorrow [Sunday] we fly to Moscow."
However, Guardiola is likely to have been encouraged by his side's performance during what was a reasonably comfortable outing in the Rhineland, with the returning Arjen Robben putting in another impressive performance.
Cologne struggled to deal with the winger for much of the game, with the Dutchman's jinking runs causing constant problems throughout.
And the 30-year old echoed the thoughts of his manager after the game, adding: "Cologne were deep, defensive and they played on the counter-attack.
"We remained quiet, letting the ball run, but we created enough chances and deserved to win at the end."