The Brazilian put the first goal past the Andalusians in the competition this season, though the Boquerones will be content to have advanced with two games to spare
A win would have ensured progression from Group C for Manuel Pellegrini's men and that was certainly on the cards when Eliseu fired them ahead five minutes before half-time.
The second half brought a change in ethos from the visitors as they looked to defend their one-goal advantage. However, they were eventually beaten when Alexandre Pato headed in an equaliser in the 73rd minute but there was to be no winning goal for either side as the points were shared.
With both teams keen to push forward, it made for an extremely open start to the game in which possession was given away far too cheaply in midfield, stopping either side from getting into any sort of rhythm.
After Eliseu failed to beat Christian Abbiati with an absurdly ambitious chip, Milan began to take hold of the game and push their opponents back.
With 19 minutes on the clock, they tested the away keeper for the first time as Bojan showed fantastic feet to wriggle between a number of Malaga shirts out on the right. Having then cut in side to create the space, he lashed an effort on goal that, despite taking a deflection, was parried aside by the stretching Willy Caballero.
The keeper then produced another inspired save as he tipped Urby Emanuelson's precise 20-yard free-kick wide. The Dutchman's effort looked destined for the top corner but Caballero had other ideas, diving to his right and getting the slightest of touches to prevent a certain goal.
The Andalusians were largely restricted to playing on the counter-attack but they still looked dangerous when Joaquin, Eliseu and Isco linked up intricately.
It was one such combination that saw Malaga strike first, five minutes before half-time. Isco shifted the ball away from Nigel de Jong before threading a diagonal ball to put Eliseu in behind. The Portuguese struck the ball first time and found the bottom corner with Abbiati rooted.
Massimiliano Allegri's side came out for the second half with much more urgency and forged a decent opportunity soon after the restart. Bojan fed Emanuelson at the edge of the box but his shot was tame and rolled comfortably into the hands of Caballero.
The visitors then began to display why they have been so difficult to score against as they put two solid lines behind the ball and squeezed the space available to the Diavolo.
But as they began to sit deeper and deeper, the pressure became too much and they conceded for the first time in the tournament. Kevin Constant exposed Joaquin's defensive frailties as he charged to the line and swung in a deep cross which Pato nodded in at the back post.
Kevin-Prince Boateng came closest to netting a decisive goal moments later but he, like many of his team-mates, was thwarted by Caballero.
The draw puts Malaga in the hat for the next round, while second-placed Milan travel to Brussels in a fortnight to face Anderlecht in a must-win fixture.