With the score level at 1-1, it was down to spot kicks to decide who would face Brazil in the final.
Lionel Messi, so often the key man for Argentina, paid tribute to Martinez.
"ÂIt was difficult at times,"ÂÂ he said. "ÂBut we have Emi and he'Âs phenomenal. We trusted him.
"WeÂ've fulfilled our objective of coming here to play every game and now we'Âre going to the final."
Martinez only made his international debut on June 3 in a World Cup qualifier against Chile and may not have not even have started at the Copa America had River Plate keeper Franco Armani not tested positive for coronavirus.
"We'Âve spent 40 days locked away, not seeing anyone outside our bubble,"ÂÂ he said after Tuesday'Âs victory. "ÂWe said on the first day we want to get to the final and what better than to play Brazil at their home.
"Brazil have a great team but we have the best in the world and we’re going there to win.”
Additional reporting by AP.