Mueller fired home with a low left-footed shot in the 58th minute as the hosts' pressure finally paid dividends.
The 28-year-old then struck again with 15 minutes remaining from an almost identical position with his right foot to seal the three points for Hamburg who moved up to 10th on 31 points.
Hertha, who had lost just once in their previous 10 league games, remain in third place on 42 points but fourth-placed Schalke moved within a point of them, with Mainz 05, in fifth, a further point behind.
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The top three teams play in next season's Champions League with the fourth-placed team playing in the competition's qualifying rounds.
Sixth place Borussia Moenchengladbach are also within striking distance on 39.
Leaders Bayern Munich protected their five-point advantage at the top after a goalless draw at second-placed Borussia Dortmund on Saturday with nine matches left in the season.
(Reporting by Karolos Grohmann; editing by Toby Davis)
