Makaay hat-trick stuns Bayern
In Italy, Milan were forced to work hard but Filippo Inzaghi's brace of goals gave them a 2-1 victory over Lens.
Depor relied on lightning breaks in Germany to dent the confidence of Bayern and provide something of a minor shock.
The opening goal came in the 12th-minute when an uncharacteristic punt by Juan Carlos Valeron found Makaay in space and he turned German international defender Thomas Linke before firing a low shot past Oliver Kahn.
Bayern came back hard, the opening goal being certainly against the run of play but Makaay was not done and on the stroke of half-time he got his second when Michael Tarnat was exposed on the right and Hector's cross was side-footed home by the Dutch star.
It was a different affair in the second period as Bayern, stung by Makaay's double, hit back and in the 57th-minute reduced the deficit when Hasan Salihamidzic took advantage of a lucky deflection to hammer home from two yards.
An Owen Hargreaves corner was headed home by Elber seven minutes later as Bayern drew level, with Victor on the line unable to keep it out.
However, Makaay had the final say when with Bayern going for the win, Depor played out a perfect counter-attack.
Valeron was at the heart of it, as he did well to control another long clearance and had the presence of mind to play an inch-perfect ball to Makaay and he out-paced the home defence and finished past Kahn to give Depor an incredible victory.
Lens did well to frustrate Milan at the Giuseppe Meazza but class eventually told and Inzaghi showed the killer instinct required to see off the French club.
Inzaghi it was who got the first, with a superb diving-header that flew just inside the corner in the 57th-minute.
It was two soon after as Rui Costa played the ball to Inzaghi and he showed great touch to turn and fire home in one movement.
The visitors got back into it as Daniel Moreira crashed in a volley from John Utaka's pin-point cross, but they did not have enough to get the equaliser and Milan held out comfortably for all three points.
Click below for more information on the games:
Champions League Group G:
Milan v Lens
Bayern Munich v Deportivo
