Mourinho, who moved from the Bernabeu to Stamford Bridge in June, gave an interview last weekend which was taken as a slight towards the Real forward in the Spanish media.
Former World Player of the Year Ronaldo had declined to engage in a slanging match with his fellow Portuguese off the pitch but on it had a big say in Real winning the eight-team exhibition tournament that has rotated around the United States.
Marcelo put the Spanish team on the scoreboard early at Sun Life Stadium in Miami with a strike from the edge of the box in the 14th minute.
Chelsea responded just two minutes later through Brazilian Ramires to level the scores at 1-1 but from then on the tournament final was the Ronaldo show.
One of his trademark free kicks in the 31st minute put Real back in front and his header from midfielder Isco's cross 12 minutes after halftime completed the scoring.
The victory maintained new coach Carlo Ancelotti's 100 per cent record in pre-season warm up games to date.
In the opening match of a doubleheader, Italian club AC Milan beat LA Galaxy 2-0 to earn third place in the tournament.
Italy striker Mario Balotelli and French forward M'Baye Niang each netted in the first half to secure the victory for the Serie A outfit.
The Galaxy had surprised many by reaching the third-place match led by Irish striker Robbie Keane and American Landon Donovan, who recently won the Golden Ball for top player at the CONCACAF Gold Cup.
Ronaldo joined Real from Manchester United for around 90 million euros (£80m) in 2009 and took his goalscoring exploits to new heights under Mourinho.
Their relationship broke down towards the end of last season, though, and after his return to London, Mourinho said he thought the world's most expensive player was a bit of a know-it-all.
In another interview last weekend, Mourinho said that aged 30, he had trained 'the true Ronaldo, not the other one, Ronaldo the Brazilian' in his time as assistant at Barcelona.
Ronaldo, though, decided to let his football do the talking.
"I prefer to remember the good things from coaches," he said on Monday. "I don't spit on the plate from which I eat and I don't speak about people who say bad things about me."