Durán began competitive driving in 2002, finishing second in the Skip Barber National series and claiming the Midwestern Champion trophy. The following year he raced in Italian Formula Renault, finishing eighth, and in the Formula Renault Eurocup, where he placed fifteenth. In 2004 and 2005 he competed in the British F3 International Series National Class with P1 Motorsport, winning the class championship in 2005 — a result that established him as a credible single-seater prospect.
The 2005 class championship success led Durán to the A1 Grand Prix series, representing Team Mexico. In the 2005–06 season he contested selected rounds and achieved a notable result by winning both races of the USA round at Laguna Seca. He returned for a second A1GP season and continued to represent his country through the latter stages of the competition in 2009, scoring a top-three finish in the final round.
In 2007 Durán joined Chip Ganassi Racing's entry in the 24 Hours of Daytona, sharing the car with Juan Pablo Montoya and Scott Pruett. The trio won the race, giving Durán a prestigious endurance victory that broadened his profile beyond single-seater categories.
After the National Class title, Durán moved up to the Championship Class of the British Formula Three International Series in 2006 with Hitech Racing. He finished tenth in the standings with 54 points, his best result being a fourth place at Silverstone.
Durán raced in the 2010 NASCAR Mexico Series for the Citizen-DHL team, securing a pole position and two top-three finishes across the season, although his overall classification was hampered by exclusions in three races.
Durán's Formula E involvement began in December 2014 when Amlin Aguri announced him as a replacement for Katherine Legge at the 2014 Punta del Este ePrix in Uruguay, the third round of the inaugural Formula E season. He deputised at short notice while Legge was committed to testing at Daytona.
For the 2015–16 Formula E season, Durán originally signed with Trulli GP, but that team withdrew from the championship before competing. He returned to the Aguri operation — by then Team Aguri — for the first three rounds of the season. At the Paris ePrix his seat was taken by Chinese driver Ma Qing Hua, who remained with the team for the rest of the campaign.
Durán's career reflects the path of many Latin American drivers who built international experience through European junior formulae and the A1 Grand Prix series before finding a niche in emerging championships. His Daytona victory alongside two high-profile teammates remains the most decorated single result of his career, while his Formula E appearances placed him among the select group of drivers who raced in the championship during its founding season.