MANCHESTER, England — It was a pinch-yourself moment for Jack Grealish, the reason essentially why he joined Manchester City.

"As soon as the game kicked off," Grealish said, "I thought to myself, 'I've actually played in the Champions League,' with the music before and everything."

And the England international looked right at home on the biggest stage in European club soccer.

Grealish marked his Champions League debut with the pick of the goals in City's wild 6-3 win over Leipzig, whose forward Christopher Nkunku scored a hat trick in vain in the teams' opening group-stage match on Wednesday.

Picking up a loose ball on the left, Grealish set off into the area, dropped his shoulder to create some space, and curled a shot high into the corner in the 56th minute. It was a strike very much befitting a player who moved for a British-record fee of $139 million from boyhood club Aston Villa.

"The goal just topped it off," the attacking midfielder said.

That made it 4-2 in an open and entertaining game at Etihad Stadium and after Nkunku slotted home from a tight angle to complete his hat trick and give Leipzig hope of a point, goals by Joao Cancelo — a long-range effort — and Gabriel Jesus secured victory for City.

"It just shows you anything can happen in the Champions League," Grealish said. "That's why it's such a wonderful competition."

Leipzig finished the game with 10 men — after the sending off of Angelino, the left back signed from City, for two yellow cards — and with its American coach, Jesse Marsch, scratching his head after a dismal defensive performance by his team in the face of wave after wave of attacks by City.

Asked about Grealish and his goal, Marsch said with a laugh: "Was that the fourth or fifth? I lost count."

Aside from some uncharacteristically sloppy defending of which Nkunku took full advantage, City was irresistible at times in the first match of its latest bid to win an elusive Champions League title, having got closer than ever last season with a loss to Chelsea in the final in Porto in May.

Nathan Ake's header from Grealish's corner put City ahead in the 16th before Leipzig defender Nordi Mukiele tried to cushion a header back to the keeper from Kevin De Bruyne's right-wing cross, only to put it into his own net in the 28th.

Nkunku headed in from close range to make it 2-1 in the 42nd but Riyad Mahrez regained a two-goal lead for City by converting a penalty in first-half stoppage time after Lukas Klostermann blocked a header by Ferran Torres with his hand.

Nkunku brought the German team back into the game again by heading home Dani Olmo's deft chip into the area past Ederson.

Completing the first Champions League hat trick by a Leipzig player couldn't stop the visitors falling to another heavy loss in Manchester, after a 5-0 thrashing by Manchester United in last season's competition.

"It's all or nothing," City manager Pep Guardiola said of Leipzig. "With them, you never think it's over."

City has scored 16 goals in its three home games this season — there were back-to-back 5-0 wins over Norwich and Arsenal in the Premier League — but Guardiola wasn't fully satisfied, with the Spanish manager seen barking orders to Grealish and in particularly Mahrez at times throughout the match, apparently unhappy at their defensive work.

It was a big win for City, considering the team travels to Paris Saint-Germain for its second Group A game in two weeks' time.

PSG started off group play with a 1-1 draw at Club Brugge, despite fielding the star-studded front three of Neymar, Lionel Messi and Kylian Mbappe together for the first time.