Zinedine Zidane's men locked horns with PSG, now managed by former Sevilla boss Unai Emery, at Ohio Stadium, but failed to impose themselves on proceedings.
The match was effectively over as a contest after goals from Jonathan Ikone (2') and Thomas Meunier (35', 40'), rendering Marcelo's 44th-minute goal nothing more than a consolation.
At Soldier Field in Chicago, meanwhile, Milan defeated Bayern following a tense battle that produced six goals in regulation time.
Bayern went into the half-time break with a slender lead, Franck Ribery and David Alaba netting for the German champions after M'baye Niang had fired Milan in front in the 23rd minute.
Milan rallied magnificently after the half-time interval, Andrea Bertolacci levelling matters before Juraj Kucka's deflected long-range effort handed the Italian outfit the lead just after the hour mark.
However, just when it seemed Milan had done enough to claim a narrow win, Bayern won a penalty at the death. Ribery stepped up and made no mistake, slotting home to send the match to a penalty shootout.
Milan went on to convert all five of their spot-kicks, while goalkeeper Gianluigi Donnarumma kept out Rafinha's effort to help secure a 5-3 penalty-shootout victory.
In the final International Champions Cup fixture of the day, Gary Cahill's 10th-minute goal proved the difference as 10-man Chelsea recorded a 1-0 win over Liverpool at the Rose Bowl in Pasadena.
Cesc Fabregas received his marching orders on 70 minutes after a horror challenge on Reds new boy Ragnar Klavan, but the sending off had no tangible impact on the result as the Blues held on for a narrow win.
Wednesday's International Champions Cup results:
Real Madrid 1-3 PSG
Bayern 3-3 Milan (3-5 pens)
Liverpool 0-1 Chelsea