Malen scored late in the first half with a low shot, and while being far from spectacular it was a crucial win for Dortmund and coach Marco Rose following their shock 1-0 loss to Borussia Monchengladbach in the Bundesliga at the weekend.
"It was hard work for us," said Dortmund defender Mats Hummels. "It was not all perfect and we made mistakes. But we had the right attitude.
"We tried everything, put in the work and so sometimes you end up winning a game 1-0."
Dortmund had fit-again captain Marco Reus in the line-up but were badly missing injured top striker Erling Haaland and, while dominating possession, they could have used his power and finishing abilities up front.
They also suffered an early setback when Mo Dahoud had to be taken off injured after five minutes, with Julian Brandt coming on in his place.
Sporting spent most of their time defending in numbers but had a few chances with captain Sebastian Coates, back from suspension, firing over the bar with his back to goal in the 31st minute.
Malen finished the move with a well-placed low shot in the 37th minute for what was also his first ever Champions League goal.
Dortmund had the ball in the net twice more in the second half but both efforts were ruled offside.
Dortmund next play Ajax in Amsterdam on Oct. 19.