Sweden star Ibrahimovic scored a hat-trick in the space of 19 first-half minutes at the Stade Constant Vanden Stock in Brussels, one of the quickest triples in the competition’s history.
He netted another in the 62nd minute, after Edinson Cavani had also found the target after the break, as PSG made it three convincing wins from three group games to close in on a last-16 berth.
Ibrahimovic now has nine goals from his last four games in all competitions, while club record summer buy Cavani has eight since joining from Napoli, and their quality was too much for Belgian champions Anderlecht, who remain without a point in the section and are staring at an early exit.
In contrast, the French club are beginning to look like genuine contenders to win the tournament for the first time, although they will face far stiffer tests than this in the months ahead.
“It was a really good game with plenty of positives all over the pitch. It was the perfect match,” declared PSG coach Laurent Blanc.
“Ibrahimovic’s four goals were exceptional. It is difficult to say which was the best.
“Winning the Champions League would be a dream for all the players and the board. But it is a difficult objective. We need to go one step at a time and the first is to win the group.”
Blanc named his strongest possible side, with the only notable absentee being captain Thiago Silva, who is still not fit again after a thigh problem.
The hosts young line-up included the 16-year-old Youri Tielemans in midfield, but they did not appear overawed in the early stages, seeking to take the game to PSG.
Salvatore Sirigu in the away goal had to turn a well-struck Matias Suarez shot around the post in the eighth minute, before Ibrahimovic managed to miss the target with just ‘keeper Thomas Kaminski to beat at the other end.
That was a sign of what was to come, and the Swede – who appears to be on a mission to win the Champions League for the first time in his career – got the breakthrough after 17 minutes, easily tapping in a low Gregory Van der Wiel cross from the right at the back post.
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The duo combined again to make it 2-0 five minutes later, the Dutch full-back’s low ball being back-heeled into the net in typical Ibrahimovic fashion at the near post.
It went from the sublime to the ridiculous as he completed his hat-trick, pouncing on a loose ball 30 yards out to hammer a ferocious first-time volley past a helpless Kaminski in goal.
Many home fans rose to their feet to applaud that effort, and it was already game over, but Anderlecht did not help themselves as they conceded again seven minutes after the restart.
Teenage Congolese defender Chancel Mbemba slipped, allowing Blaise Matuidi to square for Cavani to make it 4-0, before Ibrahimovic drove in his team’s fifth – and his 37th in the Champions League in 98 appearances – off a post just after the hour mark.
He might even have scored another but, with Kaminski off his line in the 76th minute, an attempted chip landed on the roof of the net, and he saw another shot saved towards the end.
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