Jurgen Klopp's men wasted plenty of chances to take home a healthy lead from the first leg of this quarter-final on Wednesday.
Mario Gotze was one of the prime culprits, and will be disappointed to go back to Germany with the tie still on a knife-edge.
Buoyant after downing Porto to advance to the quarter-finals, Malaga were determined to keep their Champions League fairytale alive and came out in aggressive fashion against the German champions.
Javier Saviola had an excellent early chance. Played in with a lovely flicked pass from Joaquin, the Argentine turned well in the box but could not find the target as he slammed into the side netting.
Despite pressure at the start from the Andalucians, it was Dortmund who posed the bigger threat as they attacked fluidly on the counter.
A long ball was flicked on by Robert Lewandowski into the path of Gotze, who easily broke the offside trap and advanced on Wilfred Caballero before being denied by the keeper.
The young No.10 had a similarly golden chance just minutes later, once more failing to beat the veteran shot-stopper after being fed by Marco Reus.
The next BVB man to curse his luck in front of the net was Kevin Grosskreutz, who spurned a wonderful opportunity after 29 minutes.
The midfielder was in the right place to slot Lukas Piszczek's low cross home after more intelligent approach play from Lewandowski, but with Caballero scrambling to cover his left post the shot slipped wide, sparing Malaga.
Malaga also threatened in front of their own fans, most notably with a corner that required a sterling Dortmund effort to keep the ball out.
Weligton's initial header was well saved by Roman Weidenfeller, but the rebound was steered towards the empty net and it was Gotze who popped up at the far post to head away from danger.
After the interval, Gotze's pull-back took a substantial deflection in the box, steering it into the path of Lewandowski, who looked destined to score.
The Poland international's usually razor-sharp instincts in front of goal failed him, however, and the result was a pathetic scuffed effort that once more let Malaga off the hook.
Gotze was guilty of missing a couple of glorious efforts before the break, and the playmaker's rotten luck continued as another shot failed to hit the mark.
Streaking through to meet a well-placed ball, Mario had little angle to aim at but would still have been disappointed not to test Caballero as his shot flew past the right-hand post to keep the score level.
At the other end, meanwhile, Isco appeared with a thundering half-volley that required Weidenfeller to send the ball away with his fists.