Xabi Alonso broke the deadlock with a sumptuous strike from distance in the 14th minute, but Madrid were pegged back 10 minutes later after a slack defensive sequence allowed Christian Suarez to lash home the leveller.
However, with temparatures hovering near the 40 degree Celsius mark all game, the Spanish giants laboured to establish their attacking rhythm for much of the first half.
Jose Mourinho introduced an entirely new XI after the break, and the changes marked a vast improvement in the urgency and penetration by Madrid in the attacking third, culminating with a lucky deflection off Sami Khedira for the winner in the 72nd minute.
Mourinho looked to Cristiano Ronaldo and Gonzalo Higuain to do the heavy lifting in attack, with Mesut Ozil and Granero also lining up in midfield. Fabio Coentrao and Raul Albiol also started, as 19-year-old winger Jese stood as the only unfamiliar name in the XI.
There was a hero’s welcome in Vegas, meanwhile, for Santos forward Hercules Gomez, the United States international growing up minutes away from the Sam Boyd stadium.
It was a somewhat cagey beginning from Madrid, who failed to really threaten despite winning a succession of corners early on.
Ronaldo looked a little rusty on the ball, but there were positive signs from Jese, who adopted a number of dangerous positions near the opposition box.
The Portuguese attempted to grow into the game with a powerful free-kick that forced Oswaldo Sanchez to hold on tight, and he would play a role in the opener with just under a quarter of an hour gone.
Ronaldo laid the ball off from the corner of the box to Alonso, who, from all of 30 yards, bent a superb effort low into the left side of the goal.
Madrid did not seem in any hurry to press home their advantage, though they were at least able to restrict Santos’ attacking endeavour to one or two fruitless punts forward. However, that all changed in the 26th minute as a costly defensive lapse led to the equaliser.
Alvaro Arbeloa was woefully out of sync with his fellow defenders, making a hash of an attempted offside trap and allowing Suarez to ghost in behind. The Ecuadorian took a while to sort out his feet, but kept his bearings in time to drill under the body of Casillas.
It almost went from bad to worse for Madrid past half an hour as their defense was again exposed by Santos. Gomez was allowed to slip in between Arbeloa and Raphael Varane, with only the offside flag preventing a clear opening.
Arbeloa continued to underwhelm at the back, and Suarez was allowed to slip through on goal once more, his finish coming within inches of finding the back of the net.
It was not the performance Mourinho would have wanted, as his team were unable to take advantage of a late spell of pressure around the Santos penalty area as the first-half trickled out.
The Portuguese coach rang the changes at the interval, trotting out an entirely new XI, with Karim Benzema and Kaka among those introduced to start the second half.
The two substitutes almost dovetailed superbly moments after the restart, as a tricky run and cross from the left by Kaka was hammered over by Benzema.
Madrid were attacking with far more purpose than they had done in the first-half, and Benzema was nearly on target again with a blistering drive that was tipped away by Sanchez.
Sanchez was active again, but in far less convincing fashion as he spilled a long-range drive from Callejon, and he was perhaps fortunate to see the rebound roll just wide of the post as the match crossed the hour mark.
Santos appeared to be doing enough to stay alive, but their hard work was undone after 72 minutes as Madrid took the lead thanks to a considerable slice of luck.
A corner was played to Benzema, whose shot was parried by Sanchez back into the six yard area, right off the face of Khedira and into the back of the net.
Madrid were in the ascendancy as the match neared its conclusion, but a sloppy back pass from Sergio Ramos was almost pounced on by Alonzo Escoboza minutes before the end, with only a strong block from Adan denying the Mexican side an equaliser and preserving the result.