From 2000 to 2002, Elizondo played first tournaments on the third-rate ITF Future Tour . In 2003 he made it into the top 1000 in the world rankings . He also won his first future title in doubles. Most of the time he took part in tournaments in his home country, from where he did not make the jump to the higher endowed ATP Challenger Tour . At the end of 2004 in Guadalajara he won his first Challenger win when he reached the quarter-finals. A year later in Puebla , he made it to the quarter-finals, which made him rise to 446th place in the ranking, the highest place he had in his career. In 2006 the Mexican achieved his only success in a future tournament, while he won his only title in doubles at a Challenger in León - alongside Miguel Gallardo Valles .
This was followed by a less good time, with Elizondo falling out of the top 1000 in doubles; in any case he was unable to build on his time in 2005. In 2007, Elizondo played in two games for the Mexican Davis Cup team . He won his match both times. In 2008 and 2009, however, he succeeded in pushing up again with three future titles in doubles. In addition to two semi-finals at Challengers, he was awarded a wildcard with his compatriot César Ramírez in Acapulco , so that he made his debut on the ATP Tour . They kept up well against 2 seeded Łukasz Kubot and Oliver Marach , but lost in two sets. A year later he was given a wild card along with Ramirez. This time they reached the round of 16. With the points, Elizondo rose to 297th place, making it the highest ranking in his career. After a total of 10 futures titles in doubles, Elizondo played tournaments regularly for the last time. In 2013 he returned for a match alongside Nicolás Massú in León .