“It’s impossible to have a better birthday and performance,” was Ángel Di Maria’s summation of a vintage night in Paris. It was indeed hard to imagine what more could have gone right for the French champions. Di Maria, the scorer of two goals and a particularly significant cog in a purring PSG machine, was at his irresistible best in a 4-0 demolition of Barcelona in their Champions League last 16 first leg.

The Argentina winger, 29, scored in each half, with PSG’s Germany midfielder Julian Draxler and the Uruguay striker and fellow birthday boy Edinson Cavani also finding the net as the French champions tore apart a disorganised Barcelona side who have it all to do in the return leg.

PSG, eliminated by Barcelona in the Champions League quarter-finals in 2013 and 2015, were the more aggressive side at the Parc des Princes and have put themselves in a commanding position before the 8 March second leg at the Camp Nou. The five-time European champions Barcelona have not gone out in the last 16 since losing to Liverpool in the 2006‑07 season.

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“It’s not very difficult to explain,” a shell-shocked Barcelona coach Luis Enrique said. “They were better than us from the start and put us under pressure. We couldn’t get out of it. We were obviously inferior tonight.”

Play Video 1:06 Barcelona still believe despite PSG thrashing, says Luis Enrique – video

The only downside for the PSG coach Unai Emery was the loss of the impressive Marco Verratti to a leg injury in the second half after a brilliant display from the Italy international and his fellow midfielder Adrien Rabiot in the first half. PSG were dangerous on the break and came close to scoring in the 11th minute when their captain Blaise Matuidi’s rasping shot was parried by the Barcelona goalkeeper Marc-Andre ter Stegen after a perfect through ball from Rabiot.

The home side were rewarded seven minutes later when Di Maria whipped a free kick over the Barcelona wall into the net. Barcelona continued to play their patient possession game but failed to threaten, and their complacency was punished again five minutes before the break. Lionel Messi lost the ball in midfield and Verratti slid a perfectly weighted ball to the right for Draxler, who fired a low shot into the far bottom corner of the net.

PSG started the second half strongly and went further ahead in the 55th minute when Di Maria danced around Andres Iniesta before curling a shot past Ter Stegen from 25 yards. Verratti limped off the pitch in some discomfort after 71 minutes, and was replaced by Chris Nkunku. The hosts continued to push forward, however,and a minute later Cavani, who was celebrating his 30th birthday, rifled a low shot past Ter Stegen for his seventh goal in seven games in the competition this season. The hosts also defended perfectly, with the centre back Presnel Kimpembe putting in a superb performance on his Champions League debut in the place of PSG’s injured captain Thiago Silva.

Barcelona had a chance to get an away goal seven minutes from time but Samuel Umtiti’s header hit Kevin Trapp’s right-hand post, leaving Luis Enrique’s side with a mountain to climb. No team have ever overturned a deficit of four or more goals to progress in the Champions league knockout stages.

“I’m responsible for this,” Luis Enrique said. “We might need to change our shape (for the return leg) but it wasn’t really the shape that was to blame. They are world-class players with a lot of quality. Di Maria in particular was very, very good. They have a big attacking potential, work hard in defence and are incredible on the ball.”

The PSG coach Emery, meanwhile, was full of praise for the former Manchester United man and his team-mates: “Di Maria and Cavani have great careers behind them and Draxler is still young, with a lot of things ahead of him,” he said.

“The understanding between the three of them was very high. We played a great game individually and collectively, with tremendous backing from the fans. But I still have a lot of respect for Barca and 90 minutes is long. We must keep our concentration for the return match.”