Manchester City were on the wrong side of one of the biggest shocks in Champions League history on Tuesday, while holders Paris Saint-Germain also stumbled but Gabriel Jesus helped keep Arsenal perfect.
Pep Guardiola's Man City arrived in chilly Norway for their seventh and penultimate league-phase match against modest Bodo/Glimt as hot favourites.
But they came unstuck in the freezing conditions at the stadium 200km north of the Arctic Circle, losing 3-1.
Meanwhile, PSG have work to do to ensure direct qualification to the last 16 next week after being caught out late in Portugal.
Luis Suarez struck twice for Sporting Lisbon in the second half, sealing victory with a 90th-minute header after substitute Khvicha Kvaratskhelia had equalised for PSG after 79 minutes.
The French club dropped to fifth with a home date against Newcastle in their last group stage fixture.
While the top eight secure direct entry to the last 16, teams placed ninth to 24th must navigate an additional two-legged play-off to join them.
Next week the league phase comes to a dramatic denouement with all 18 matches kicking off at the same time.
Real, under new coach Alvaro Arbeloa, produced a dazzling attacking display to help fans forget recent disappointments.
Kylian Mbappe struck twice against his former side and Vinicius Junior – jeered by his own fans during a home win over Levante last weekend –scored a brilliant goal to lift the record 15-time European champions from seventh to second behind unstoppable Arsenal.
Jesus was on cloud nine after two close-range finishes in the first half to help guarantee the Gunners a top eight finish.
"It's a dream night," said the 28-year-old.
"I always dreamed of being a footballer. I watched when I was a kid. I watched a lot of Serie A, so to be here in this stadium and score here is tears in my eyes because I always dreamed of being here."
Arsenal's joy in Italy contrasted with despondency in Norway for Premier League heavyweights Man City.
Kasper Hogh's first half-brace and a second half strike from Jens Petter Hauge at the ecstatic Aspmyra Stadion triggered a seismic upset.
Rayan Cherki replied after Hauge's goal, but Rodri's dismissal for two bookings left City in tatters and facing a long trip home.
While the pitch may have been artificial there was nothing false about the result, Bodo/Glimt's first group stage win which gave them hope of making the play-offs.
"Everything has started to be, since the new year, against us in many, many things," said Guardiola.
"I know how good a team Bodo are. I didn't underestimate them. There is not much I know but they reached the semifinal last season of the Europa League and they were fresh in mind.
RESPITE FOR TOTTENHAM
"We arrived in some departments without important players who give consistency to the team. They are a little bit fragile, as they were last season in a certain period.
"How they fought 10 against 11, a lot of players made a step up, but we have to change the dynamic quick for the next game against Wolves and after that for the last game against Galatasaray."
Elsewhere there was some much needed respite for under-fire Tottenham boss Thomas Frank as Spurs beat Borussia Dortmund 2-0 to move into automatic qualification territory for the knock-outs.
Copenhagen held Napoli t a 1-1 draw, Olympiacos beat visitors Bayer Leverkusen 2-0, Ajax defeated hosts Villarreal 2-1 and Kairat Almaty were in no danger of registering their first three points of the campaign as the bottom side of the 36-team table were swept aside 4-1 by Club Brugge.
On Wednesday, matchday seven concludes with Mohamed Salah back for Liverpool after finishing fourth with Egypt at the Africa Cup of Nations with Arne Slot's side at Marseille.
Chelsea's new boss Liam Rosenior's first taste of Champions League football is a home game against Pafos while runaway Bundesliga leaders Bayern Munich welcome Union St-Gilloise.