America trailed Herediano by three goals heading into the semi-final second leg at the Estadio Azteca but levelled the tie after just 18 minutes, while Dario Benedetto struck four times as the hosts took control in Mexico.
A first-half red card to Herediano's Edder Nelson put the visitors even further on the back foot, while Alejandro Diaz wrapped up America's win with five minutes remaining.
The emphatic comeback saw America qualify for their sixth final in the history of the CONCACAF Champions Cup and Champions League combined, with the Liga MX club having won their five previous deciders.
Gustavo Matosas' side will face Montreal Impact in the final, which will be held over two legs on April 22 and 29.
The match could have started much differently, as Herediano missed two massive chances in the opening minute.
America goalkeeper Hugo Gonzalez saved Yendrick Ruiz's shot with his boot and a follow-up effort flashed wide of the post.
Just three minutes later and the home side were on the scoreboard when a flowing move saw Darwin Quintero tee up Benedetto and although the latter's shot was saved, the former tucked the loose ball away.
Benedetto struck in the eighth minute in spectacular fashion, receiving a pass on the edge of the area before curling his shot into the top corner of the net.
The home side equalised the tie in the 19th minute when Quintero cleverly set up Benedetto for a classy first-time shot, while the Argentine striker notched his hat-trick after Herediano failed to clear a corner six minutes later.
Benedetto was involved in everything, with Nelson shown a straight red card in the 27th minute for kicking the 24-year-old forward, and he scored his fourth goal just after the half-hour mark thanks to a smart cut-back from Miguel Samudio.
America led 5-3 on aggregate at the break and although they slowed down in the second half, Diaz capped off the emphatic victory with a tap in from Martin Zuniga's cross in the 85th minute.
