Dortmund won their first three games of the year, but there was plenty of criticism after last week's poor performance in a goalless draw at Heidenheim.
Malen got Dortmund's opener in the 16th minute after he received a pass from Niclas Füllkrug and fired an unstoppable effort into the net on Friday.
He completed his brace before the break and thanks to 12 minutes of added time after the game was interrupted for some 10 minutes when fans threw tennis balls and chocolate coins onto the pitch in protest against the entry of an investor into the German football league (DFL).
In the second half, the game was also shortly interrupted a few times due to the protests.
Dortmund had clear chances to add a third, first in the 52nd when Noah Atubolu stopped Füllkrug at point-blank range.
Ian Maatsen's first-time shot hit the post in the 72nd, while Malen missed the chance to complete his hat-trick when he pulled his shot narrowly wide of the far post in the 74th.
The ball was eventually again in the back of the net in the 87th as Atubolu couldn't stop Füllkrug's furious header.
Coach Edin Terzic linked Sancho's fitness issue to his months-long absence from games at United before he returned to Dortmund on loan last month.