The 27-year-old France forward opened the scoring in the 14th minute, producing a composed finish from just inside the penalty area.
The strike took his European tally to 71 goals in 99 appearances, moving him level with Real Madrid great Raul in joint-fifth place on the all-time Champions League and European Cup list.
Only Cristiano Ronaldo (140), Lionel Messi (129), Robert Lewandowski (109) and Karim Benzema (90) have scored more in the competition.
Real Madrid doubled their advantage nine minutes later after a costly error from Inter goalkeeper Josep Martinez. The Spanish keeper misplaced possession following a back pass from Benjamin Pavard, allowing Federico Valverde to win the ball and calmly steer it across the line.
Inter had started brightly, forcing Thibaut Courtois into saves from Hakan Çalhanoglu and Lautaro Martinez as the Real goalkeeper marked his 100th Champions League appearance for the club. Former Liverpool midfielder Curtis Jones also struck the crossbar.
Martinez redeemed himself before the interval with a double stop against Mbappe and Jude Bellingham, while the post denied another effort. Bellingham later missed a chance to make it 3-0.
Carlos Augusto pulled one back in the 77th minute, creating a tense finale. Despite the win, Real’s supporters voiced their frustration at their side’s display.
“It could have ended 5-1 or 6-1 for us. It could also have ended 6-6. I don’t want to say that Inter won the game because we created more and in crucial moments, like the two chances Jude had before and after the break,” said Mourinho.
“It was a crazy game, and I don’t like that kind of madness. I prefer to score 5, 6, or 7 but with absolute control and without needing an absolutely incredible performance from the goalkeeper.
“In today’s game, whoever decides the best player on the field must have been asleep, because if they don’t give Courtois the best player award today, they never will (laughs). Without taking credit away from Fede, who won it.
“It was difficult to play with Trent, whom I greatly appreciate for the work he did, but his characteristics as a midfielder and the physical demands of playing as a full-back or midfielder are different.
“As a coach, I couldn’t do the things I would like to do. If you see Inter’s goal, it’s clear that we had already lowered our defensive intensity and didn’t have too many players who could help us control the game differently.
“We were very good when we were compact. Valverde’s goal wasn’t a coincidence but a great interpretation of the structure and strategy we had.
“We played against a great team with many options that increased their intensity with the substitutions. It was a tough match with three crucial points.
“We are three points closer to qualifying, and I am absolutely convinced we will qualify, but getting these three points early is important.”
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