He played in Major League Baseball (MLB) for the Kansas City Royals and Cincinnati Reds.

He earned his first major league hold on September 22 by pitching a scoreless seventh inning against the Cleveland Indians.

He made his MLB postseason debut in the American League Wild Card game vs the Oakland Athletics on September 30, 2014.

[14] In 2015, Finnegan began the season with the Omaha Storm Chasers of the Triple–A Pacific Coast League, working as a starting pitcher.

[16] On July 26, 2015, Finnegan was traded to the Cincinnati Reds, along with John Lamb and Cody Reed, for Johnny Cueto and cash considerations.

[16] Finnegan began the 2016 season pitching out of the rotation for Cincinnati, opening as the team's second starter behind Raisel Iglesias due to a plethora of injuries.

However, in one of his losses, Finnegan threw a complete 8 innings against the Los Angeles Dodgers, giving up one run and losing to Clayton Kershaw's two-hit shutout.

Finnegan began the 2017 season in the Reds rotation, but on April 15, he was placed on the disabled list with a shoulder injury.

However, on June 27, in his first start back off the disabled list against the St. Louis Cardinals, he re-injured his shoulder and had to leave the game.

[22] In 2021, Finnegan spent the year with the Triple-A Louisville Bats, recording a 5.53 ERA with 57 strikeouts in 55.1 innings of work across 40 games.

[26] However, prior to the season on April 17, Finnegan signed with the Kansas City Monarchs of the American Association of Professional Baseball.