The result leaves Madrid, under new head coach Xabi Alonso, on top of Group H with four points while Pachuca are eliminated after two defeats.

Saudi club Al Hilal, who held Real in their opener, face second-placed Salzburg later on Sunday.

The Spanish giants were in trouble after just seven minutes when Raul Asencio was shown a straight red card after he pulled down Salomon Rondon with the Venezuelan clear on goal.

That left the Liga MX team sensing the chance for an upset in front of 70,248 fans at the home of the NFL's Carolina Panthers.

Pachuca quickly went close when Brazilian Kenedy saw a shot parried out by Thibaut Courtois and the Belgian keeper did brilliantly to deny Alan Bautista's follow up shot.

But Real were able to get a grip on the game in midfield and slow the pace down, limiting opportunities for Pachuca.

It was a superbly worked team goal that provided the breakthrough for Madrid in the 35th minute.

Gonzalo Garcia's clever flick released Fran Garcia down the left and he looked inside to Jude Bellingham who took the ball in his stride and then buried a left-foot shot into the corner.

Two minutes before the break Real doubled their advantage when Trent Alexander-Arnold drilled a low cross in from the right and Arda Guler collected Gonzalo's deft lay-off and fired home.

Pachuca created a pile of chances after the break, peppering Courtois's goal, but the Belgian was up to the task denying Brazilian substitute John Kennedy and efforts from Rondon and Bryan Gonzalez.

Javier Eduardo Lopez missed the best opportunity for the Mexican side, firing wide after some sloppy defending from Madrid.

The outcome was put beyond doubt in the 70th minute when Federico Valverde slid the ball home after a smart exchange with Brahim Diaz.

Pachuca finally got some reward for their determined effort when Elias Montiel's shot on the turn was deflected off Aurelien Tchouameni and flew past the wrongfooted Courtois.

Alonso, who tasted victory for the first time as Real coach, praised the way his team handled the early setback.

"We had to be defensively, for almost all the game with one player less and it became really intense for us, but we defended with a lot of sacrifice and solidarity which is what it takes," he said.

"We waited for our chances, so I was really pleased with the performance with a player less," he added.

The Real coach said he was pleased to see his team's ability to change plan during a game.

"We want to have the culture that we understand situations, the structure, the context and we understand what it takes in each moment, with strong principles.

"I think that game intelligence gives you another edge and today I am pleased how they understood the quick change in the cooling break that we had," he added.

Pachuca coach Jaime Lozano said his team had failed to make the most of the extra man.

"We had a great start, (but) we did not make the most of our advantage. They have the strongest players in the world and their players were amazing. Their strongest feature is that they don't need to play at their best to win any match, they were amazing," he said.