The hosts were gifted the chance to break the deadlock in just the 11th minute when Pavel Krmas was penalised for tripping Ragnar Klavan in the box, allowing Paul Verhaegh to fire home from the penalty spot.
Freiburg struggled to produce a response as Augsburg dominated the first half and threatened to secure a big advantage before the interval.
The pattern of the match continued in the early stages of the second half as the hosts piled the pressure on Freiburg's vulnerable defence.
Altintop should have added to his personal tally after beating two defenders on an impressive solo run, but Roman Burki responded well to get a strong hand to his low effort.
Krmas headed wide late on as Freiburg looked for a way back into the game, but it would prove to be a comfortable afternoon for Augsburg.