Leipzig scored late on to snatch a 4-3 victory at Istanbul Basaksehir while Krasnodar defeated Rennes to claim their maiden win in the Champions League.
Nordi Mukiele and Yussuf Poulsen put Leipzig two-up before Irfan Kahveci pulled one back in Istanbul.
Dani Olmo restored the two-goal buffer for Leipzig but Kahveci was not done yet and scored twice (on 72 and 85 minutes) to complete his hat-trick and level the scores.
However, in injury time, Alexander Sorloth scored his first goal for Leipzig to earn his side the win.
The Bundesliga outfit joined Group H leaders Manchester United on nine points, with Paris Saint-Germain - who are playing the Red Devils at Old Trafford later on Wednesday evening on six points.
Meanwhile, Marcus Berg scored the only goal of the game in Russia to give Krasnodar the three points.
Not only was the result a first victory at the highest club level in Europe for Krasnodar, it also secured third place in Group E and a place in the Europa League knockout stage.
Rennes remain without a win in what is also their maiden term in the Champions League.
About 10,000 fans were in the Krasnodar stadium - at the UEFA limit of 30 per cent of capacity due the coronavirus pandemic restrictions - in a rare European game not played in an empty stadium this season.