Elías is the third member of the Elías family to compete in motorcycle racing. He entered the 125cc World Championship in 2000 at age 17, finishing third in the 2001 season and taking his first win at the Dutch TT in Assen. He moved to the 250cc class for 2002, recording three consecutive top-four championship finishes (4th, 3rd, 4th) between 2002 and 2004.
Elías stepped up to MotoGP for 2005 with Fortuna Yamaha, then joined Gresini Honda for 2006 and 2007 alongside Marco Melandri. His sole premier-class win came at the 2006 Portuguese Grand Prix at Estoril on 15 October. Starting the final lap third, Elías made an aggressive braking move at the first corner to pass both Valentino Rossi and leader Kenny Roberts Jr., briefly losing momentum when he clipped Roberts. Rossi retook second, and it appeared the Italian would hold on. But Elías drafted Rossi through the final corner and edged him at the line by just 0.002 seconds — one of the closest finishes in MotoGP history. The result cost Rossi five points, exactly the margin by which Nicky Hayden beat Rossi in the 2006 championship. Elías remained the last non-factory rider to win a premier-class race until Jack Miller's 2016 Dutch TT victory for Marc VDS.
His 2007 season was compromised by a broken leg sustained in a crash at Assen. He spent 2008 with Alice Ducati before returning to Gresini Honda in 2009.
When the Moto2 class replaced 250cc in 2010, Elías moved to Gresini on a Moriwaki machine. Despite a heavy pre-season crash threatening his preparation, he was immediately competitive. His campaign turned at Le Mans, where he won a chaotic race to take the championship lead — a position he never surrendered. Elías clinched the inaugural Moto2 World Championship at the Malaysian Grand Prix with three rounds still to run, establishing himself as the first champion of what would become Grand Prix racing's primary feeder class.
Elías returned to MotoGP in 2011 with Team LCR on a Honda RC212V, but the season was his weakest at that level: 61 points and fifteenth in the championship. He returned to Moto2 in 2012 with Aspar before the relationship ended after Mugello. He subsequently substituted for the injured Hector Barbera at Pramac Ducati across several rounds during the second half of the season.
Elías moved to the United States for 2016, joining Yoshimura Suzuki in the MotoAmerica Superbike Championship. He won three consecutive races as a substitute early in the season. The 2017 campaign was dominant: ten victories and eighteen podium finishes, never finishing lower than second in any race where he took the checkered flag, delivering him the Superbike championship title. He finished third in the 2016 standings (304 points, six wins) and runner-up in both 2018 and 2019, each time behind champion Cameron Beaubier. He accumulated 32 career MotoAmerica wins and 60 podium finishes for Suzuki before announcing his retirement from the series at the close of 2020. He made a brief comeback attempt in 2023 before retiring mid-season.
Elías stands as one of the defining figures of the transition era in Grand Prix motorcycle racing. His inaugural Moto2 title gave the new class instant prestige, while his Estoril MotoGP win altered the course of a world championship in one of the most dramatic finishes the sport had produced. His subsequent MotoAmerica career demonstrated sustained speed at the highest level of American Superbike racing across nearly a decade of competition.