Play at Estadio Eladio Rosabal Cordero in Heredia was brought to a halt for almost five minutes as tempers boiled over following the sending off of America striker Michael Arroyo in the 27th minute.
Arroyo received his marching orders after a studs-up challenge on Cristian Lagos, bringing both benches to their feet amid a mass of pushing and shoving.
When play resumed, Herediano made their numerical advantage count via three unanswered goals in the second half as the Costa Rican outfit moved within touching distance of their first appearance in the final.
Esteban Ramirez made the breakthrough eight minutes after half-time, curling the ball beyond America goalkeeper Hugo Gonzalez from the edge of the penalty area.
With America pushing numbers forward, the visitors were exposed on the break 16 minutes later when Yendrick Ruiz looped a header over Gonzalez.
It got better for Herediano in almost identical situation with eight minutes remaining, Argentinean substitute Jonathan Hansen directing a header into the bottom corner of the net.
The return leg is scheduled for April 8 at Estadio Azteca in Mexico City.
'I have found myself again. At Manchester United, I continued working mentally and physically - I was preparing for this moment' United star provides insight to difficulties at Old Trafford
'When I came to Madrid, I thought that I was Messi and Cristiano in one body – I was a punk, a nobody': Real Madrid star reflects brutally on his younger self
