Gutiérrez began racing karts in Mexico in 2004. In 2007 he stepped into single-seaters with the Formula BMW USA series, finishing second overall with four wins and earning Rookie of the Year honors. He then moved to Europe for the 2008 Formula BMW Europe season — the championship's inaugural year after the merger of the British and German series — and won it convincingly by 26 points from Marco Wittmann, recording seven victories, six of them consecutive, from sixteen races.
For 2009 he joined ART Grand Prix in the Formula 3 Euro Series alongside Jules Bianchi, Valtteri Bottas, and Adrien Tambay, finishing ninth overall. He also competed in two rounds of the British Formula 3 championship, taking a podium at the Algarve International Circuit against a field that included Daniel Ricciardo.
In 2010, Gutiérrez moved to the newly formed GP3 Series with ART Grand Prix and won the inaugural championship with two rounds to spare, scoring five wins and eight podiums from sixteen races. At 17 years and approximately nine months when he clinched the Formula BMW Europe title in 2008, he became the youngest Mexican driver to win an international racing championship up to that point.
He then contested the GP2 Series from 2011 to 2012. Racing for Lotus ART (later Lotus GP), he was partnered with Jules Bianchi in 2011 and finished thirteenth in the championship. In 2012, alongside James Calado, he improved to third in the standings with 176 points, three wins, and five fastest laps — becoming the first GP3 Series graduate to finish in the top three of the GP2 championship.
Gutiérrez made his Formula One race debut at the 2013 Australian Grand Prix alongside Nico Hülkenberg at Sauber. He scored his first and only championship points finish at the 2013 Japanese Grand Prix, where he climbed from fourteenth on the grid to seventh place at the flag, holding off Nico Rosberg in the closing laps. He also set a fastest lap in Spain that season, placing him among the youngest drivers to have set a fastest lap in Formula One history.
In 2014 he remained at Sauber but did not score points, and his drive was not renewed for 2015.
In December 2014 Gutiérrez was announced as Scuderia Ferrari's test and reserve driver for 2015, filling the seat left vacant by the death of Jules Bianchi.
Gutiérrez joined the new Haas F1 Team for 2016 alongside Romain Grosjean in what was the team's debut season. He did not score points across the season and left the team in November 2016.
In July 2018 Gutiérrez joined Mercedes AMG as a simulator driver and was subsequently named a reserve driver in both Formula One and Formula E. He performs regular simulator work at the team's factory, contributing to car development in support of the race drivers. In 2024 he was named a brand ambassador for Mercedes in Formula One.
In early 2017 Gutiérrez competed in selected Formula E rounds with Techeetah, replacing Ma Qing Hua from the fourth round onwards. He raced at the Mexico City, Monaco, and Paris ePrix, finishing inside the top ten twice. Later in 2017 he made seven IndyCar Series appearances for Dale Coyne Racing, standing in for the injured Sébastien Bourdais.
During the 2020 COVID-19 pandemic Gutiérrez competed in several prominent esports events including the F1 Esports Virtual Grand Prix Series and The Race All Stars, taking multiple wins and podium finishes.
Gutiérrez is the founder of EDASI Drive, the licensed Formula One merchandise distributor for Latin America. His younger brother José Gutiérrez is also a professional racing driver.