Izazola, the 19-year-old forward who made his Mexican first-division debut for Pumas on February 13, gave Mexico a 3-1 lead five minutes after entering the game in the 35th, and Rivera added another in the 49th for Mexico, which will try for an 11th CONCACAF title on Sunday.
Chivas forward Ulises Davila scored the first goal and created the danger that resulted in an own-goal as Mexico withstood some early Panamanian possession before eventually prevailing.
Panama, which qualified for the U-20 World Cup for the fourth time with its quarterfinal victory over Honduras on Wednesday, will play Sunday in the third-place game with the final berth in the Pan American Games at stake.
Panama had the early possession and even a chance in the 11th minute that Mexican keeper Carlos Lopez had to block with his feet , but his Panamanian counterpart Kevin Melgar also was active, racing out of his penalty area in the 12th to clear a potentially threatening through ball.
Davila, who had a goal in Mexico's 3-0 opening win over Cuba, capitalized on a defensive mix-up to put El Tri ahead in the 14th with its first shot.
Panamanian teammates Manuel Vargas and Oscar Linton nearly collided at the top of the defensive third, Alan Pulido got a foot to the loose ball and Davila dribbled to just outside the penalty arc before unleashing a right-footed drive that had Melgar diving to his left.
Panama equalized 14 minutes later. Josue Flores cross from the right bounced once in the area, Javier Caicedo took it off the chest and volleyed it on the drop with Carlos Orrantia behind him and Kristian Alvarez in front but unable to react quickly enough.
It was the first goal allowed by Mexico in four games in the championship.
Davila helped put Mexico back in front in the 31st, taking a throw-in from Saul Villalobos, chipping the ball over the head of Panamanian defender Manuel Vargas and then looping a ball laterally into the middle of the area.
With no one challenging him at his own six-yard box, Linton inexplicably dove to head the ball over his own net but put it past Melgar.
With the lead restored, Mexican manager replaced Taufic Guarch and Pulido with Rivera and Izazola in the 34th and 35th minutes
It was Rivera's fourth appearance in the tournament, all as a substitute, but only Izazola's second.
Orrantia set up both for their goals, sending in a cross that Izaola headed in standing at the edge of the six, and then ran down the right before sending a rolling ball that Rivera volleyed from on top of the penalty spot.
Mexico continued to dominate with Rivera being denied twice more: a headed bouncing ball cleared off the line by Linton, and another blocked by Melgar. Melgar also made an athletic save to deny Izazola a second in the 63rd.