On August 27, 2013, Beliveau was recalled by the Rays from the Triple-A Durham Bulls. He did not get into any games before being optioned to the Double-A Montgomery Biscuits on August 29. He was recalled on September 21 after an 18-inning game against the Baltimore Orioles. In 2014, Beliveau made 30 relief appearances and posted a 2.63 earned run average and 28 strikeouts in 24 innings.[6] In 2015, he made five appearances for Tampa and had a 13.50 earned run average.[6]
Baltimore Orioles
Beliveau signed a minor league contract with the Baltimore Orioles on December 5, 2015.[7] He spent the 2016 season with the High-A Frederick Keys and the Double-A Bowie Baysox, where he had a combined 4–0 record, 2.54 earned run average, and 66 strikeouts in 492⁄3 innings.[8] He elected free agency following the season on November 7, 2016.[9]
Toronto Blue Jays
On December 15, 2016, Beliveau signed a minor league contract with the Toronto Blue Jays that included an invitation to spring training.[10]
Beliveau started the 2017 season with the Triple-A Buffalo Bisons. He was called up by the Blue Jays on June 5, 2017, while the team was in Oakland.[11] On July 22, Beliveau was designated for assignment. He cleared waivers and was outrighted to the Buffalo Bisons on July 25.[12] On October 13, Beliveau elected free agency.[13]
Cleveland Indians
On November 22, 2017, Beliveau was signed by the Cleveland Indians to a minor league contract with an invitation to the club's 2018 spring training camp.[14]
Beliveau's contract was purchased by the Indians on April 26, 2018.[15] He was designated for assignment on May 4, 2018, outrighted to the Columbus Clippers on May 7, and had his contract purchased again by the Indians on May 29. Beliveau was later designated for assignment again on June 2 and outrighted once more to Columbus on June 5. He was released by the organization on August 8, 2018.