The 27-year-old is set to join league rivals Schalke 04 on a four-year deal at the end of the season after spending five years at the club.
Martin Harnik started the farewell party by firing Andre Breitenreiter's side ahead four minutes into the encounter.
With five minutes left before the interval, Sane connected with Pirmin Schwegler's free-kick to double the hosts' lead.
Niclas Fullkrug completed a perfect first half for the Reds with the third goal in the 42nd minute.
Davie Selke's 73rd minute stood as consolation for Hertha Berlin who suffered their 10th league defeat of the campaign.
Late in the game, Sane was replaced by Josip Elez while Nigeria's Noel Sarenren-Bazee was introduced for Kenan Karaman in the 86th minute.
Hannover are placed 13th in the Bundesliga log with 39 points 33 games - nine points above relegation playoff spot.
They visit Bayer Leverkusen for their last league match of the season on May 12.