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The Colombian gave Bayern a fourth-minute lead at the Parc des Princes and then pounced on slack defending to score again just after the half-hour mark.
However, the former Liverpool winger was then shown a red card in first-half stoppage time following a rash challenge on Hakimi, which forced PSG's Moroccan star off in tears.
Joao Neves pulled one back for PSG, but Bayern held on despite playing the entire second half a man down.
That in part illustrates the impact on PSG of losing the attacking thrust of all-action right-back Hakimi.
The German side's sensational start to the campaign has seen them win all 16 games in all competitions, they have scored 56 goals altogether and are one of only two clubs with 12 points in the 36-team standings in Europe's elite competition alongside Arsenal.
