Lionel Messi scored twice as Paris Saint-Germain (PSG) came from behind to beat RB Leipzig while Liverpool survived an Atletico Madrid fightback to win 3-2 during the Union of European Football Associations (UEFA) Champions League group matches on Tuesday.

At the Parc des Princes, Messi scored twice and Kylian Mbappe sparkled but later missed a penalty as PSG came from behind to beat RB Leipzig 3-2.

Leipzig were ahead through goals from Andre Silva and Nordi Mukiele as PSG suddenly looked disjointed.

But Messi was set up by Mbappe for the equalizer and then deftly chipped in a 74th-minute penalty awarded for a foul on the France striker. Mbappe's missed spot kick proved unimportant.

PSG top Group A with seven points but Manchester City bounced back from their defeat in Paris in the last matchday by crushing Club Brugge 5-1 in Belgium.

Pep Guardiola declared City's win "one of the best performances in Europe we've done so far" after Riyad Mahrez scored twice and 19-year-old Cole Palmer was among City's scorers.

Much of the night's drama happened at the Wanda Metropolitano in Madrid, where Mohamed Salah scored another impressive goal, twisting away from a string of Atletico defenders before his shot deflected in off James Milner to open the scoring.

Naby Keita doubled Liverpool's lead with a stunning volley, but Atletico hit back with French international Antoine Griezmann scoring twice to fire up the home crowd.

Just as Atletico seemed to have the upper hand, Griezmann was given a straight red card for a high boot in the face of Roberto Firmino.

A seesawing game was decided from the penalty spot in the 78th minute as Salah sent Jan Oblak the wrong way after Mario Hermoso pushed Diogo Jota. The Egyptian's 31st Champions League goal makes him the club's top scorer in the competition, overtaking Steven Gerrard.

Atletico were then denied a penalty when the referee studied the VAR and decided Jota had not fouled Jose Maria Gimenez.

Liverpool manager Jurgen Klopp told BT Sport, "We played a really solid second half in a tough game with intense football from both teams.

"We got the penalty, then there was a red card, and obviously, it was in our favor."

The Reds are top of Group B with three wins out of three while Atletico are equal on four points with Porto as Colombian winger Luis Diaz scored the only goal to beat AC Milan 1-0 in Portugal.

Diaz, who had earlier hit the post, netted midway through the second half as Porto were rewarded for their dominance in a game in which they missed several chances and barely gave Milan a sniff at the other end.

Borussia Dortmund had an off night, as they were beaten 4-0 by Ajax at the Johan Cruyff Arena in Amsterdam.

Former West Ham striker Sebastien Haller scored his sixth Champions League goal in three games as Ajax took an iron grip on Group C with a maximum of nine points. Dortmund are second on six points.

Karim Benzema netted for Real Madrid as the 13-time winners thrashed Shakhtar Donetsk 5-0 in Kiev on the eve of the start of his trial in France on charges of complicity in blackmail.

Benzema, who is due to go on trial in France on Wednesday in the "sex tape" case involving his former international teammate Mathieu Valbuena, scored the final goal in Real's rout of Shakhtar in a match played in Kiev.

A first-half own goal from Serhiy Kryvtsov put Real on their way before Vinicius Junior scored two superb goals and set up Rodrygo for the fourth before Benzema completed the job.

Inter Milan ended Sheriff's perfect start to their debut Champions League campaign with a comfortable 3-1 win at San Siro.

Goals from Edin Dzeko, Arturo Vidal secured the Italians' first victory in Group D.

(With input from agencies)