Arturo Vidal was shown two yellow cards by referee Anthony Taylor after Inter’s penalty claims were waved away.
Eden Hazard converted an early spot kick for Real, with Achraf Hakimi scoring an own goal.
Antonio Conte’s side are rooted to the bottom of Group B with just two points from four games.
The win for Zinedine Zidane’s men moves the thirteen-time European champions up into second place in the group, one point behind leaders Borussia Monchengladbach.
Gladbach cruised to a 4-0 victory over Shakhtar Donetsk in the earlier kick off, scoring three first-half goals to boost their hopes of qualifying top of the group.
A mountain to climb for Inter Milan
If Inter thought the task to reach the knockout stages was tough before Real arrived at the San Siro, it became abundantly clear within the first seven minutes it was about to get a whole lot harder.
Nicolo Barella’s clip on the calf of Nacho put Conte’s side under pressure immediately, with English referee Taylor pointing to the spot without hesitation.
Former Chelsea man Hazard, who had yet to to score a Champions League goal for the Spanish champions, powerfully converted the penalty low to Samir Handanovic’s left-hand side.
Real, who were missing key men Sergio Ramos and Karim Benzema for the tie, were too much too handle for The Nerazzurri in the opening half and should’ve doubled their advantage on two occasions.
Lucas Vazquez saw his powerful drive smack against Handanovic’s far post, then Ferland Mendy chose to square the ball to Vazquez instead of shooting after brilliant build up play by the French defender.
Vidal’s moment of madness came on 33 minutes when Inter’s appeals for a penalty were dismissed by Taylor. As the players gathered around to protest, the Chilean midfielder received his first yellow card.
As Vidal pushed his way through the small ground of players, he found himself face-on to Taylor, which was enough for the Premier League referee to pull out a second yellow card and send an angry Vidal off the pitch.
Despite a slight resurgence from Inter Milan in the second half, Real never looked in danger of conceding the win, which was rubber stamped when Rodrygo latched on to Vazquez perfect cross to the back post.
The Brazilian winger’s rifled shot was turned in by full-back Achraf Hakimi to pile more misery on the Italian club.
Inter Milan remain winless in this year’s competition and in severe danger of continuing their run of not reaching the knockout stages since 2011-12.
For Zidane’s Real Madrid, back-to-back victories over Inter this month have edged the Spanish side closer to qualifying for the last 16 for a record 25th time.