Mame Biram Diouf opened the scoring in the seventh minute for Hannover before Rafael van der Vaart equalised from the spot in the 13th minute.
Szabolcs Huszti converted a penalty for Hannover in the 39th minute and Ya Konan made it 3-1 in the 45th minute before deciding the match for good with his second goal after 68 minutes.
Mohammed Abdellaoue added a fifth in the 85th minute.
The result saw Hannover continue their strong home form to improve to 33 points while Hamburg saw their modest two-match winning streak snapped to remain on 34 points.
Hannover went ahead through a set piece with Huszti sending his free kick into the box where Diouf headed in from seven yards out.
Hamburg equalised six minutes later from the spot as Van der Vaart struck in to the lower left corner after Johan Djourou was ruled to have fouled Dennis Aogo in the area.
Hannover reclaimed the lead with a penalty of their own with Huszti hammering the ball into the upper right corner after Hamburg keeper Rene Adler brought down Sergio Pinto.
The Hannover goalscorer injured his left thigh while scoring and was immediately substituted after successfully converting Hannover's 15th consecutive penalty in the Bundesliga.
Ya Konan increased the lead in the 45th minute with a volley from 25 yards out.
Diouf missed a great chance to make it 4-1 two minutes into first half injury-time but headed just wide before shooting past the post.
Ya Konan showed him how it is done in the 68th minute, poking home a pass from Konstantin Rausch from the left side.
Abdellaoue added his name to the scoring sheet with five minutes left after a pass from Artur Sobiech.