The northerners, who had lost their last two games and had failed to win at home since the Dutchman took over in September, cancelled out a 28th-minute Hanover lead with Milan Badelj's long-range volley three minutes later.
Maximilian Beister's header straight after the restart put them in the driving seat and the forward turned provider to set up Hakan Calhanoglou for their third goal from a tight angle as Hanover slumped to their sixth straight away defeat this season.
Hamburg move up to 11th on 15 points while Hanover, without a win in their last seven league games, ended the game with 10 men after Salif Sane was sent off with a second booking and dropped to 13th on 14 points.
Leaders Bayern Munich protected a four-point lead over second-placed Bayer Leverkusen on Saturday by easing past Borussia Dortmund 3-0, who dropped to third, seven points off the pace.
(Reporting by Karolos Grohmann; Editing by Clare Fallon)
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