Ivo Ilicevic shot over the crossbar from 30 yards after 12 minutes, but the visitors were always relying on Calhanoglu’s dangerous free-kicks and Marwin Hitz denied him from 20 yards in the 18th minute.
Then, in the 25th minute, another whipped delivery from the 20-year-old attacking-midfielder led to the best chance for Westermann who snatched at the shot which went wide.
Typically, as Hamburg’s season has panned out, Augsburg got a second on 32 minutes with Hahn assisting Altintop who raced clear of Milan Badelj to tuck past Rene Adler.
Adler’s form has been on a constant dip this season and his failed attempt to punch clear Hahn’s tame 25-yard strike saw Augsburg take a three-goal advantage on 42 minutes.
Within two minutes, Hamburg had reduced the deficit to two when Calhanoglu’s inswinging delivery clipped Westermann on the way through to eventually beat Hitz.
More was expected from Mirko Slomka’s side, but it was Augsburg who continued to play on the front-foot.
Alexander Esswein missed a brilliant chance to add a fourth on 53 minutes, followed up by a fine Adler stop to deny Altintop his hat-trick after the hour mark.