Falling behind early to an Eden Hazard penalty, the Nerazzurri were left reeling after midfielder Arturo Vidal was sent off for dissent with only half an hour played at the Stadio Giuseppe Meazza.
Lucas Vazquez rattled the woodwork and Rodrygo tucked home a second after the break for a much-changed Real Madrid, as Inter never looked like threatening Thibaut Courtois’ goal. The defeat leaves Antonio Conte’s side without a win in the competition and a monumental task to qualify.
Real Madrid got off to a flyer and were ahead through a penalty with less than 10 minutes gone. Martin Odegaard threaded through for Nacho and as he looked to pull the trigger, the Spaniard was clipped by Nicolo Barella. Hazard made no mistake from the spot, despite Samir Handanovic going the right way.
It was almost 2-0 just minutes later as Vazquez saw a low strike from range crash off the frame of the goal with Handanovic beaten.
The visitors were dominating and got in again as Ferland Mendy raced clear in the box, but the full-back cut the ball behind Luka Modric with the goal at his mercy.
Inter finally fashioned a chance with 20 minutes gone, but despite some quick movement on the edge of the box, Vidal could only blaze over as the ball was rolled into his path.
However, the Nerazzurri’s task was made all the more difficult with a moment of madness from Vidal. The Chilean went down in the box but after Anthony Taylor waved his claims for a penalty away, the midfielder confronted the referee and was booked. Just seconds later Vidal’s aggressive demonstration at Taylor saw him given a second yellow and his marching orders.
Inter began the second half brightly as they chased an equaliser, and Stefan De Vrij saw a close range effort blocked after meeting Romelu Lukaku’s header across the face of goal from a corner.
Yet the Spaniards doubled their advantage shortly before the hour mark to all but seal victory. Vazquez timed a run behind the defence to perfection to latch onto Toni Kroos’ reverse pass and his cross to the back post was drilled home emphatically by substitute Rodrygo, netting with his first touch.
Meanwhile, the dangerous Vazquez could only fire into the side-netting after meeting a floated freekick at the back post, whilst at the other end Ivan Perisic curled a bending effort just wide, as Inter struggled for opportunities.
Although Perisic had Courtois at full strength with a low shot late on, Real Madrid were comfortable in seeing out victory to move into second in the group, whilst Inter remain bottom.