Altintop struck twice before Andre Hahn gave Augsburg a comfortable three-goal lead. Heiko Westermann did reduce the arrears for Hamburg just before the interval, but it was nothing more than a consolation for a side who must now win their final two games of the season to stand any chance of surviving.
Augsburg got off to a dream start when Paul Verhaegh's cross evaded two Hamburg defenders, allowing Altintop to place a first-time volley beyond the reach of Rene Adler. It was the 22nd time this season Hamburg had conceded the opening goal and from that point on it was always going to be an uphill struggle for the guests.
Hakan Calhanoglu posed Hamburg's main threat, principally from set pieces, and one such free-kick sent Augsburg keeper Marwin Hitz scampering across his goal to make the save at full stretch.
Altintop at the double
HSV suddenly sensed their chance, with Westermann having a header blocked and lifting the rebound over, before Milan Badelj was denied by the excellent Hitz. A goal was in the air, yet it came at the other end of the pitch as Altintop, Slomka's first signing as coach of FC Schalke 04 in 2006, made it two from Hahn's delivery, beating Adler on the volley.
Things got even worse for Hamburg in the 42nd minute when Adler got both hands to Hahn's speculative effort, but still failed to do any more than help it on its way into the back of the net. Before the half was over, though, Westermann got the slightest of touches on Calhanoglu's curling free-kick with his shoulder to guide it beyond Hitz and provide the visitors with a timely boost.
Augsburg hold firm
Only twice in Hamburg's uninterrupted 51-year presence in the top flight had they recovered from three goals down to win - 1977 in Cologne and 1964 against MSV Duisburg - and it was going to take something historic to salvage anything in Augsburg. They had a chance to make it interesting when Westermann placed a free header wide from close range, but in throwing everything forward left themselves open to being punished by Augsburg on the break.
Altintop glanced a header wide after a sustained period of pressure, instigated by that close shave which was a warning that the game was far from over. Alexander Esswein sent efforts either side of Adler's goal as the Red Shorts were forced to gamble. Dong-Won Ji then lacked the composure to wrap things up with only Adler to beat, but a fourth goal was not necessary as Markus Weinzierl's men took the points.
Line-ups and statistics
Although he let in three goals, Rene Adler also made an amazing save in the Top 5 Saves, courtesy of the official Bundesliga YouTube channel: