Mario Gotze was the main culprit for the visitors, spurning three golden openings, as his side failed to find a way past the impressive home goalkeeper, Willy Caballero, at La Rosaleda.
The away draw still leaves Jurgen Klopp’s side in a strong position ahead of the home leg, but the boss will know the tie could have been wrapped up already.
Instead Malaga, who, for all their opponents’ dominance, still caused Dortmund the odd nervy moment, will travel to the Westfalenstadion still in with a shout of the last four.
Malaga had the first chance when Javier Saviola ran onto a clipped pass down the right of the area, got to the byline and cut inside, only to opt to go for the near post rather than the far and dragged his shot wide.
But it didn’t take long for Dortmund’s attacking triumvirate of Robert Lewandowski, Gotze and Marco Reus to start exerting their influence as Dortmund started to open their hosts up almost at will.
Gotze ran clear on to a Lewandowski header as the Malaga backline appealed in vain for offside, but his shot lacked power and Caballero dived to make a one-handed save.
The Germany international then got in one-on-one down the right of the area, but Caballero was again equal to his side-footed shot.
Reus then brought another save out of the ‘keeper after neat link-up play and a low shot from the edge of the area.
The hosts showed they could still be a threat when Dortmund netminder Roman Weidenfeller had to be quick off his line to get to the ball ahead of Saviola.
Their defence, though, continued to live dangerously and Weligton was booked for pulling back Lewandowski right on the edge of the area, Reus curling the resulting free-kick wide.
But Malaga ended the half in the ascendancy.
Weidenfeller, under no pressure, spilled a Joaquin cross and Dortmund’s Felipe Santana scrambled the ball away to spare his team-mate’s blushes.
But the ‘keeper redeemed himself with a fine save to keep out a Weligton header from a Joaquin corner.
Lewandowski fluffed another golden chance for Dortmund minutes after the break, skewing his shot horribly wide when Gotze’s cut-back found him in plenty of space in front of goal.
Gotze then fired wide of the far post after racing on to a measured pass down the right as another opportunity came and went for the Germans.
At the other end, Isco’s drilled effort was parried away well by Weidenfeller, but it was Dortmund who left the pitch at full-time with a feeling of what might have been.
MALAGA: Willy, Jesus Gamez, Demichelis, Weligton, Antunes, Toulalan, Iturra, Joaquin, Saviola (Francisco Portillo 67), Isco (Duda 87), Julio Baptista (Cruz 76).
BORUSSIA DORTMUND: Weidenfeller, Piszczek, Subotic, Felipe Santana, Schmelzer, Gundogan, Kehl (Bender 79), Reus (Schieber 69), Gotze (Kirch 90), Grosskreutz, Lewandowski.
Referee: Jonas Eriksson (Sigtuna).