scored a sensational hat-trick and the fastest two goals in
The 18-year-old had his double after just six minutes and 14 seconds at the Santiago Bernabeu before teeing up Karim Benzema to make it four, after Sergio Ramos had chipped in a penalty.
Benzema then added a fifth late in the second half, leaving Rodrygo to complete his incredible treble in injury-time.
He doesnt surprise me, said Madrid coach Zinedine Zidane. He has a bit of everything. He is intelligent, he learns very fast and wants to learn and improve.
Physically he has to get better but technically, he knows how to do everything with the ball.
Madrids emphatic victory means they are virtually qualified from Group A, sitting five points ahead of Club Brugge, even if Paris Saint-Germain who are top look certain to claim first place.
It means Zidanes side will likely be at the mercy of the draw when it comes to the last 16 but that is their punishment for a miserable opening defeat in Paris and an equally dispiriting draw at home to Brugge.
Yet the knock-out stages are far away and Rodrygo is the man of the moment.
After scoring the fastest ever league goal by a Real debutant in September - a sumptuous control and finish after 94 seconds - he now has his name etched into the European record books too.
Today my dream came true, Rodrygo said.
Hes not afraid, said Benzema. He enjoys the ball and I love a player that plays like that.
Benzema made his own piece of history by equalling and then surpassing Alfred di Stefanos 49 European Cup goals but the way he hoisted Rodrygo to celebrate his first suggested he knew this was the teenagers night.
When club president Florentino Perez presented Rodrygo to the fans last summer, he said they had signed one of the worlds great prodigies, a year after Vinicius Junior had also arrived from Flamengo.
Determined to avoid a repeat of losing out on Neymar to Barcelona, Madrid flooded Brazil with scouts, each of them instructed to find the next young gems.
They found Vinicius, who excelled last season but has struggled since the arrival of Eden Hazard, and Rodrygo, who stayed at Santos for a year before finally joining in June.
He was supposed to be introduced gradually to the senior team by playing first for Castilla, the clubs B team, and there was confusion earlier this season when one weekend he turned out for neither.
He is a first team player, Zidane said. We know exactly what were doing with him.
Rodrygo replaced Vinicius to make his debut against Osasuna but his four consecutive starts have come in the absence of Gareth Bale, who is recovering from a calf injury and may struggle to regain his place when he returns.
There will be sturdier opponents than Galatasaray, who offered Madrid a way back into this group by losing 1-0 at home last month and put up precious little resistance here.
But Rodrygos two early finishes were ruthless, both set up by Marcelo crosses from the left. The first he cushioned and steered back inside, leaving Mario Lemina on the floor, before guiding a shot into the far corner.
The second was more simple, a leap and a well-timed header past Galatasarays goalkeeper Fernando Muslera.
In the 14th minute, it was three. Prompted by VAR, referee Felix Zwayer decided Steven Nzonzi had caught the foot of Toni Kroos inside the area and Ramos lifted his penalty down the middle.
There was still time for Benzema to add a fourth before half-time as Rodrygo capitalised on an error from Yuto Nagatomo and played a perfect pass for the Frenchman to score.
The rest of the match was a procession, with Casemiro and Hazard both taken off, rested for the trip to Eibar on Saturday.
Benzema scored his second late on, tapping in from close range to make it five, before Rodrygo raced in from the left, exchanged passes with the Frenchman, and poked in.
After the final whistle, he kissed the matchball as he left, while the fans chanted his name.
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Should out of form Proteas captainTemba Bavuma be droppedfor Thursdays T20 World Cup clash against Pakistan?
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No - He is our captain and dips in form happen to everyone.
Yes - Temba is nowhere right now and he needs to stand down if we are to have any chance of winning.
No - He is our captain and dips in form happen to everyone.
Yes - Temba is nowhere right now and he needs to stand down if we are to have any chance of winning.
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