The sides had been locked at 0-0 following extra time in Saturday's match in Doha.
Pachuca won the shootout after missing their first two penalties to become only the second CONCACAF team to reach the final of the competition against European champions Real, which takes place at the Lusail Stadium on Wednesday.
Neither team could find the net in 120 minutes, with Pachuca struggling to create any real attacking threat after an exciting first half in which the Egyptians dominated possession.
Pachuca's Carlos Moreno made a number of fine saves to deny the Africans the lead and, despite adjustments and substitutions by both coaches, the match went to extra time and penalties.
Pachuca started the shootout poorly as Salomon Rondon's effort was saved by Mohamed El-Shenawy and Borja Baston missed.
All was not lost, however, as Mahmoud Kahraba's shot was later saved by Moreno and Omar Kamal's spot kick went wide.
Faber Gil put the Mexicans 6-5 ahead and nerves were frayed when Khaled Abdelfattah hit the bar to Egyptian dismay.
"It was difficult, very complicated, especially because of the marathon game we played today," said Pachuca coach Guillermo Almada. "We'll try to get the players back on their feet and go into the game (final) with all the motivation in the world."
"Confidence is the last thing to die, we had confidence in our team, in the players who were going to score, in Carlos, who became the star, he deserved it," added midfielder Pedro Pedraza.
"We had an atypical tournament and he is the first to deserve it, because of him we won the championship (CONCACAF Champions Cup)."
It is the Mexican side's fifth appearance at a FIFA competition. Their best performance came at the 2017 Club World Cup when they finished third.
Champions League holders Real are the most prolific Intercontinental Cup winners with five titles followed by fellow Spaniards Barcelona, Corinthians and Bayern Munich. Last year's trophy went to Manchester City.
