Sánchez attended Blanca Malaret High School in Sabana Grande, Puerto Rico. After graduating in 2000, Sánchez pitched for four seasons at Ohio Dominican University in Columbus, Ohio. While at the university, Sánchez threw four no-hitters and set school records for most strikeouts in a single game (sixteen), most strikeouts in a single season (105), most strikeouts in a career (311), and most shutouts in a career (ten). However, his final collegiate appearance was arguably his worst, as he was saddled with the loss in the Panthers’ NAIA regional playoff defeat to Saint Vincent College, going five innings and allowing six runs on six hits.

Sánchez was promoted to the Single-A Augusta GreenJackets of the South Atlantic League in 2005. He went 5–7 with a 4.08 ERA in twenty-five starts, but he led the South Atlantic League in strikeouts with 166, averaged 11.9 in nine innings pitched, and was selected to the league’s All-star team. During the offseason, Sánchez pitched for the Carolina club of the Puerto Rican Professional Baseball League, posting a 2–2 record with a 2.91 ERA in 19 relief appearances.

Coming into 2006, Sánchez was ranked as the sixth best prospect in the Giants’ organization by Baseball America. He began the 2006 season with the Double-A Connecticut Defenders, where in thirteen appearances (three starts) he went 2–1 with a 1.15 ERA and forty-six strikeouts.

Sánchez was called up to the Giants on May 26, 2006, as a reliever. He made his MLB debut two days later on May 28 against the Colorado Rockies. He pitched one inning in relief and retired all three batters he faced (Todd Helton, Matt Holliday, and Garrett Atkins). His performance was overshadowed, however, because Barry Bonds hit his 715th home run in the same game to surpass Babe Ruth for second place on the all-time home run list.

Entering the 2007 season, Sánchez was ranked as the second best prospect in the Giants’ organization (behind only Tim Lincecum) by Baseball America. Sánchez made the Giants’ roster out of spring training. He struggled in his first fourteen games, however, and was sent down to Fresno on May 21 when Russ Ortiz came off the disabled list. Sánchez returned to the majors on June 6 when, coincidentally, Ortiz got hurt again. On June 13, he picked up his first major league hit (an RBI double) in a 7–4 loss to the Toronto Blue Jays. On July 4, he was placed on the disabled list with a strained rib cage, but he was reactivated on July 18.

In 2008, Sánchez made the Giants’ starting rotation out of spring training as the fifth starter. In only his second start of the season, he struck out a career high ten batters against the San Diego Padres in a game the Giants eventually won 1–0. Sánchez struck out ten batters again in a 3–1 victory against the Cincinnati Reds on April 25, becoming the first Giants left-handed pitcher since Shawn Estes to strike out at least ten batters in a game more than once in a season. From May 28 through June 12, Sánchez won a career best four straight starts. On June 12, in a 10–7 victory over the Colorado Rockies, he became the first Giants’ starter to allow seven runs and win a game since Russ Ortiz did it in 2000. In his next start, on June 17 against the Detroit Tigers, Sánchez took a no-hitter into the sixth inning, but he was ultimately the losing pitcher in a 5–1 loss. Sánchez finished the first half with an 8–5 record and 115 strikeouts, which were the most ever in the first half of a season by a Giants’ left-hander during the Giants’ tenure in San Francisco.

Sánchez was again the fifth starter in the Giants’ rotation in 2009. The season did not start well for him, though, as he had a 2–8 record in the first part of the year. On June 28, Ryan Sadowski replaced him in the rotation.

Sánchez was chosen to pitch for Puerto Rico in the 2009 World Baseball Classic. He made two starts in the Classic. He won the first one on March 11 by pitching four scoreless innings in a 5–0 victory over the Netherlands. Although he only pitched 2⁄3 innings and gave up three runs in his next start against the United States, he was in line for the win going into the ninth inning. However, J. C. Romero and Fernando Cabrera blew the lead, and the United States knocked Puerto Rico out of the Classic with a 6–5 victory.

Sánchez was arbitration eligible to begin 2010, but he avoided arbitration by signing a one-year contract with the Giants. He was named the fourth starter out of spring training this time. Sánchez began started strong in 2010, as he was 7–6 by the All-Star break. Because of injuries to the Giants’ left-handed relief pitchers, Sánchez made his only relief appearance of the year on July 30 in a 6–5 win over the Los Angeles Dodgers. On August 3, Sánchez tied Juan Marichal’s record when he struck out seven straight batters in a 10–0 win over the Colorado Rockies. Two months later, on the last day of the season, Sánchez started against the San Diego Padres. Sánchez pitched five shutout innings, scored the first run after hitting a triple in the third inning, and was the winning pitcher in a 3–0 win. The win sent the Giants to the playoffs for the first time since 2003.

Sánchez throws a fastball that travels about ninety-one mph for his main pitch, though it sometimes can go up to ninety-five mph. His other pitches (slurve and change-up) travel in the low eighties. Wildness has been a problem for Sánchez; he has walked 10% – 15% of major-league batters faced each season. However, he also strikes out a lot of batters; he struck out two hundred for the first time in his career in 2010. That year, he led all qualifying MLB starting pitchers in limiting hits per innings pitched (6.61 H/9), and his career swinging-strike percentage is among the best in the majors.

On November 7, 2011, Sánchez was traded to the Kansas City Royals with prospect Ryan Verdugo for outfielder Melky Cabrera. He struggled with the Royals, pitching to a 1-6 record and 7.76 ERA in 53 ⁄3 innings, while allowing 65 hits, including eight home runs, and 44 walks. After allowing seven runs on seven hits and one walk in 1 ⁄3 innings in a start against the Seattle Mariners, the Royals designated Sánchez for assignment on July 17, 2012.

The Pirates signed Sánchez to a minor-league deal on February 6, 2013. The deal included an invitation to spring training. Sanchez made the team and was in the starting rotation to begin the season. On April 26, 2013, he was ejected for the first time in his MLB career by umpire Tim Timmons after intentionally pitching at St. Louis Cardinals batter Allen Craig following back-to-back home runs by Matt Carpenter and Carlos Beltrán and a single by Matt Holliday. After posting an 11.85 ERA with the Pirates, he was designated for assignment on April 30, and was later released on May 8.

On May 13, 2013, Sánchez signed a minor league contract with the Los Angeles Dodgers. After spending a month at the Dodgers extended spring training location in Arizona, Sánchez joined the AAA Albuquerque Isotopes on June 24. He made 14 starts and was 7-3 with a 5.13 ERA.

On December 18, 2013, Sánchez signed a minor league deal with the Chicago Cubs. He was released on July 2, 2014.

On January 29, 2016, Sánchez signed a minor league deal with the Cincinnati Reds. He was released on March 18.

In December 2016, Sánchez signed a minor league contract with the Kansas City Royals. He was released on March 20, 2017.

On June 30, 2018, Sanchez signed with the York Revolution of the Atlantic League of Professional Baseball.

On March 7, 2019, Sanchez signed with the Saraperos de Saltillo of the Mexican League.