Both sets of supporters also threw firecrackers on to the pitch several times while some briefly clashed with police prior to the game as they tried to force their way into the stadium.
An announcer repeatedly urged them to stop, with flares banned in German grounds, and the clubs could face sanctions.
"I have no understanding for this rivalry," Hanover president Martin Kind told reporters.
Borussia Dortmund are already being investigated by the German FA after their fans lit flares during their 3-1 league win at Schalke 04 two weeks ago.
(Reporting by Karolos Grohmann)
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