Liverpool-bound Naby Keita opened the scoring as Hamburg's 100 percent winning start to the Bundesliga season ended following a 2-0 defeat at home to RB Leipzig.
Keita will move to Anfield next summer and gave an indication of why the Reds have overhauled their transfer record to land him after breaking the deadlock in the 67th minute with a long-range thunderbolt.
The Guinean collected the ball 30 yards from goal and shook off the challenge of Walace before rifling into the top corner and beyond a helpless Christian Mathenia.
Hamburg, who had seen off Augsburg and Cologne before the international break, went in search of a leveller but were hit on the counter eight minutes later as Timo Werner made the game safe for last season's runners-up.
After the visitors had cleared their lines from a corner, the German striker latched onto the loose ball and shrugged off the desperate tackles of two defenders to go through on goal before coolly slotting home.
Victory in northern Germany lifts Leipzig onto six points after three games, the same number as their beaten foes.