Without Lionel Messi to provide creative inspiration or score in crucial moments, Ronald Koeman's side were simply abject, a pale shadow of their former rip-roaring selves.
The Bavarians found the breakthrough just after the half-hour mark when Muller's effort took a deflection off Eric Garcia.
In-form Lewandowski then doubled their advantage with a tap-in after Jamal Musiala's shot pinged off the upright, before bagging a second in similar fashion as Serge Gnabry hit the post too.
The reigning Bundesliga winners, pretty much like in their 8-2 demolition job last year, outclassed their Spanish rivals from stem to stern. With a little more cutting edge, the scoreline would've been much bigger.
Barcelona, regretfully, have lost their identity as a club.
Here are the player ratings for both sides:
Marc-Andre ter Stegen - 6.5/10
He denied Sane twice in an incredible display of goalkeeping, but Ter Stegen stood no chance with any of Bayern's goals tonight.
Ronald Araujo - 7/10
The young Argentine star came of age with a mature performance tonight, blocking so many shots in the first-half. He also made five clearances on the night.
Gerard Pique - 7.5/10
The Barcelona stalwart tried every trick in the trade tonight in stopping Bayern's in-form attackers, but to no avail. However, it doesn't take away any credit from his heroic display - five clearances, two blocked shots, four tackles, six ground duels won, five long-balls, and 95% passes completed!
Eric Garcia - 6/10
He struggled to contain Lewandowski, catching him with a poor challenge early on before the Pole broke free of him in a wonderful attacking move. Oh, and Muller's effort also deflected off the centre-back.
Sergio Busquets - 6.5/10
The Barcelona skipper struggled to control the midfield as the game essentially flew past him. Koeman put him out of his misery in the 59th minute was taking Busquets off.
Sergi Roberto - 6/10
Another disappointing performance, Roberto was in sixes and sevens all night, struggling to get his act together against Bayern's fast-moving play. He, too, went off with Busquets just before the hour mark.
Jordi Alba - 5/10
Completely off the pace, sloppy in passing and easily dispossessed (23 times to be exact), Alba looked every bit like a spent force tonight. Are his days at the top now numbered?
Frenkie de Jong - 6.5/10
Often the playmaker for Barcelona, De Jong, too, was below his best tonight. His passing was accurate as always but nothing meaningful really came of it.
Pedri - 6.5/10
Euro 2020's best young player was a shadow of his talismanic self which took the competition by storm a few months ago. He sure passed the ball around well and ran his socks off, but his overall impact was minimal.
Luuk de Jong - 5/10
Not the most memorable debut for the Dutchman, who had an ineffectual outing for Barcelona. He made only 23 touches on the ball in 66 minutes of action and failed to muster a single shot.
Memphis Depay - 6/10
In terms of work-ethics at least, Depay was better than his international teammate. But as far as direct threats are concerned, he, too, was subpar. The flair with which he's played so far was totally lacking tonight.
Yusuf Demir - 6/10
The youngster replaced Roberto and could hardly put up a better performance.
Gavi - 6.5/10
His positional sense was good and looked confident.
Philippe Coutinho - 6/10
The estranged Barcelona midfielder had hoped to conjure something against his old club but failed to produce anything of note.
Oscar Mingueza - 6/10
He read the game well and even looked to set up Depay at one point with a lunging ball, but it was dealt with comfortably by Neuer.
Alejandro Balde - 7/10
Fearless, audacious and full of vigor, Balde was a breath of fresh air. Arguably the best Barcelona substitute of the night.