The 22-year-old Spaniard bagged Barcelona's final goal against the Mexican side at Zayed Sports City, pouncing on an angled through ball from Andres Iniesta to sidefoot home from eight metres in the 67th minute.
Pedro had already scored in in La Liga, the King's Cup, the European Champions League and the Spanish and European Super Cups.
Barcelona, who had to come from a goal down, will go on to face Libertadores Cup winners Estudiantes in the final.
"I'm going to give my shirt to my family," Pedro told reporters. "I played my usual game waiting for the chance to score. I was calm.
"(The victory) cost us quite a lot...but we created chances, we got some goals...got to the final, which will be another hard match."
His coach Pep Guardiola also paid tribute to the young striker, who has proved an able foil to Ballon D'Or winner Lionel Messi and record signing Zlatan Ibrahimovic in Barcelona's all-conquering team.
"Pedro is very good of course," Guardiola told the post-match news conference. "The job was done by all the players. What (Pedro) did is very important, his goal was so good."
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