Rodrygo struck 10 minutes from time to earn Real Madrid a 3-2 win and deny Inter after the visitors had battled back from two goals down in Tuesday's Champions League clash.
Madrid head coach Zinedine Zidane labelled the Group B match a "final" and his side made a bright start thanks to Karim Benzema and Sergio Ramos – the latter scoring his 100th goal for the club.
Inter, who entered the contest one point better off than their opponents, battled back through well-taken strikes from Lautaro Martinez and Ivan Perisic either side of half-time.
But Madrid regained their lead late on when substitutes Vinicius Junior and Rodrygo combined on the counter, making it one win in seven for Inter and under-pressure boss Antonio Conte.
Marco Asensio was denied by a smart Samir Handanovic save and Nicolo Barella scraped the top of the crossbar with a header in a lively and end-to-end start to the showdown.
That set the tone for what was to follow as Benzema pounced on Hakimi's underhit backpass, rounded Inter goalkeeper Handanovic and tucked the ball into an empty net for the 25th-minute opener.
Ramos added a second for Madrid eight minutes later by getting away from his marker to meet Toni Kroos' corner and head in from the edge of the six-yard box.
Inter gave themselves an instant lifeline as Barella superbly flicked the ball into the path of Martinez to pick out the bottom-left corner 10 minutes before the interval.
Conte's Inter, once again without injured striker Romelu Lukaku, initially struggled to get at their opponents in a quieter second half in the Spanish capital.
However, against the run of play, Martinez nodded the ball into the path of Perisic and the makeshift striker held off Lucas Vazquez before rifling across Thibaut Courtois.
Both teams went in search of a winner and it was Madrid who found it – Vinicius leading a break down the left and feeding the ball to fellow Brazilian Rodrygo, who took a touch to set himself and then found the top-right corner to win the match during the closing stages.
What does it mean? Madrid off the mark, Inter bottom
This could prove to be a truly massive victory for Madrid, with this first Group B win moving them onto four points from three matches, two more than bottom side Inter.
Borussia Monchengladbach now lead the way after crushing second-placed Shakhtar Donetsk 6-0 earlier on Tuesday, meaning it is very much all to play for in a tight group.
Inter, who were second best in terms of possession (45 per cent) and shots on target (three to Madrid's seven), head into the reverse fixture with Zidane's men knowing that they will surely need a win to keep alive their hopes of progressing.
Ramos reaches a century
Three days after making his 500th LaLiga appearance, Ramos crossed off another milestone with his 100th goal for Madrid in all competitions – 55 of those via his head.
He also won more aerial duels than any other player on the pitch (three) and turned over possession eight times, which was second only to Casemiro among Madrid's players.
Hakimi's horror moment
Madrid's decision to let Hakimi join Inter in the close season raised eyebrows given the full-back's impressive form during his time on loan with Borussia Dortmund.
He topped the charts for tackles (three) and crosses (four) for Inter, highlighting his importance at both ends of the pitch, but his lapse in concentration for Benzema's opener will be the defining moment of his match.
Key Opta Facts
- Real Madrid have won seven of their eight home matches against Inter Milan in European competition (L1), winning each of the last six.
- Madrid have conceded two or more goals in five consecutive Champions League games for just the second time (also in 2001).
- Only Lionel Messi (70) and Cristiano Ronaldo (63) have scored more group-stage goals in the Champions League than Karim Benzema (49).
- Sergio Ramos netted his 100th Real Madrid goal in all competitions, with 55 of those being headed.
- Since the start of last season, only Robert Lewandowski (11) and Serge Gnabry (6) have scored more away goals in the Champions League than Inter Milan's Lautaro Martínez (5).
Madrid travel to Valencia on Sunday in their final LaLiga outing before the international break, while Inter make the trip to Atalanta in Serie A on the same day.