The Polish striker scored two quick goals in the opening minutes of the second half, followed by 17-year-old Lamine Yamal becoming the youngest Clasico scorer. Captain Raphinha sealed the victory with a late goal, leaving the Bernabeu crowd in shock.
Barca stretched their lead at the top with 30 points, six above Real who saw their unbeaten LaLiga run come to a bitter end after 13 months, leaving them one tantalising positive result away from equalling the Catalans' league record of 43.
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After four consecutive Clasico defeats, Barcelona claimed their first triumph over Real since March 2023 in style with a clinical performance in which they were true to coach Hansi Flick's ideas of gambling with an aggressively high defence.
The visitors were more than comfortable playing on the counter-attack, exploiting the lightning speed of Raphinha and Yamal to help feed LaLiga top scorer Lewandowski.
Real were on top at the start but became frustrated as they wasted several chances, mainly through off form Kylian Mbappe who missed four clear opening from close-range and was caught offside nine times, including having two goals ruled out.
Despite Real dominating proceedings, Barca kept playing their risk-taking tactics and the gamble paid off when Lewandowski silenced the crowd with a two-goal blitz in the 54th and 56th minutes to reach 14 goals in 11 league games.
The hosts tried to get back into the contest but their batch of missed opportunities continued with Vinicius Jr, Jude Bellingham and Mbappe wasting clear openings that infuriated their fans, who started booing the players.
Barcelona kept playing their game and it was a matter of time until they ended the contest with two more goals on the counter through the precocious Yamal after 77 minutes and the ever dangerous Raphinha six minutes from time.
"We are very happy, very happy. To win here like this is a great victory," Lewandowski told DAZN. "The season is long, but this victory can help us with a lot more, with confidence and football ... so far we haven't won anything, but the important thing is that we have a clear idea, we know where we want to go on."
Mbappe's off key performance will have increased the growing concern in the Spanish capital over the France captain's slow start at Real since he arrived from Paris St Germain in June.
Three of the eight goals he has scored for Real in his first 13 games were penalties and he has found the net only once in the last five matches in all competitions.
Mbappe has struggled to connect with Vinicius Jr, Bellingham and Rodrygo up front, raising questions over how he fits into a Real team who have just enjoyed a successful season without him, having won a Champions League and LaLiga double.
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