In 2007, he played for the Boise Hawks and Peoria Chiefs, going a combined 4–6 with a 5.83 ERA in 21 games (10 starts).

Alburquerque was assigned to the Triple-A affiliate Toledo Mud Hens following spring training, where he appeared in 4 games, with a 1.93 ERA and 10 strikeouts in 42⁄3 innings pitched.

[6] Following the 2011 season, it was discovered that Alburquerque had suffered a non-displaced stress fracture in his right (throwing) elbow.

He had a screw inserted during surgery performed by Dr. James Andrews, and had an expected recovery time of 6–8 months.

He made his 2012 debut with the Tigers on September 4 against the Cleveland Indians, pitching 11⁄3 scoreless innings and striking out one batter.

[10] At the major league level, he made eight appearances during the regular season and posted a 0.68 ERA.

Alburquerque was on the playoff roster for the American League Division Series against the Oakland Athletics.

In a moment of levity, he kissed the ball before flipping it softly to Prince Fielder at first to complete the play.

[16][15] On January 24, 2015, Alburquerque and the Tigers avoided arbitration agreeing on a one-year, $1.73 million contract.

[24] In 6 appearances for the Triple-A Tacoma Rainiers, he logged a 6.00 ERA with 6 strikeouts across 6 innings pitched.

[25] On January 7, 2017, Alburquerque signed a minor league contract with the Kansas City Royals that included an invitation to spring training.

[32] On January 18, 2018, Alburquerque signed a minor league deal with the Toronto Blue Jays.

Alburquerque did not play in a game in 2020 due to the cancellation of the Mexican League season because of the COVID-19 pandemic.

[36] In 2021, Alburquerque pitched to a 0–1 record with a 2.78 ERA in 24 relief appearances, striking out 26 in 22+2⁄3 innings of work.

[37] On February 16, 2023, Alburquerque signed with the Long Island Ducks of the Atlantic League of Professional Baseball.

[40] On July 19, 2024, Alburquerque signed with the Long Island Ducks of the Atlantic League of Professional Baseball.

His strikeouts per 9 innings pitched ratio is above the league average, sitting at 10.7 through the end of the 2017 season.