A late Neri Cardozo winner sealed the title for Monterrey in a game that appeared headed for extra time.
Monterrey will represent CONCACAF at the FIFA Club World Cup in December.
"Every one of these guys put in their little bit of effort," Victor Manuel Vucetich said. "This title has a special flavor to it."
Santos came out of the gate firing, knowing it needed to overturn a 2-0 deficit from the first leg. The home side created a number of chances, but was denied several times by Monterrey goalkeeper Jonathan Orozco, who looked to be in fine form.
"Santos is a very deserving rival that put us in a bind and played their best soccer," Orozco said. "We were able to find ourselves with that goal that gave us the title. We came here with that intent, to go out and win. Santos pushed us back, they're a great rival, but we were able to do our thing."
Just seconds before halftime, Santos found the opener thanks to a fantastic strike from Daniel Ludueña, who turned and fired past Orozco from the top of the box after some great build up.
Santos leveled the tie on aggregate five minutes after the restart after Darwin Quintero beat two men down the right flank and crossed the ball for Oribe Peralta, whose sidefooted volley beat Orozco after a scramble in the box.
Monterrey found a dramatic winner in the 81st minute when Neri Cardozo played a quick one-two with Walter Ayovi, collected on his chest and fired a deflected shot past Oswaldo Sanchez, who had no chance after a slight deflection off his own defender.
"We deserved it," Angel Reyna said. "It got tough, but thank God we were able to pull through it. I'm enjoying this moment."
The goal gave Monterrey a 3-2 aggregate lead, but because it was an away goal, it virtually ended the tie, as Santos was left needing to score twice in the last 10 minutes.
"I hope that the fans go to the airport to greet the team," Humberto Suazo said.
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