It was announced this week that the highly-rated Lewandowski had turned down the offer of a new contract with Dortmund and that he would be leaving the club within the next 18 months, sparking talk about where his next destination will be.
However, he is still very much a Dortmund player at present and he struck twice in the opening 21 minutes on Saturday to put his side in charge.
Mohammed Abdellaoue pulled a goal back for Hannover in the 40th minute but Julian Schieber made it 3-1 midway through the second half as Dortmund got back to winning ways following last weekend's league draw with Borussia Monchengladbach and their midweek cup quarter-final loss to Bayern Munich.
Hannover came into the match having collected two wins and a draw from their previous three games but they faced an uphill battle on Saturday after falling behind after only eight minutes
Jakub Blaszczykowski threaded a through-ball to Kevin Grosskreutz, who played it onto Lewandowski and the Poland international blasted home from 10 yards out.
Hannover thought they had equalised soon after but Konstantin Rausch's effort was ruled out for offside, and to compound their misery Dortmund made it 2-0 in the 21st minute.
The same trio who made the first goal were involved again as Blaszczykowski crossed to Grosskreutz, whose shot was saved by keeper Ron-Robert Zieler but he could only block the effort straight to Lewandowski who slotted home for an easy finish.
Hannover pulled a goal back five minutes before the break when Abdellaoue took advantage to head home after Dortmund had failed to deal with a free-kick into the box.
The hosts created a number of chances as they sought to settle the match with Santana, Lewandowski and Mario Gotze going close.
The reigning champions did finally manage a third goal in the 72nd minute when Schieber and Blaszczykowski combined for the former to fire home from 12 yards.