The lefty pitched a scoreless eighth inning in a 5-4 walk-off win that marked Philadelphia's season-high sixth straight win.
Alvarado had been sidelined since May 8 with left elbow inflammation. The 28-year-old has allowed one earned run in 15 appearances over 15⅓ innings, striking out 26 and walking none.
Alvarado recently pitched two innings in two rehab appearances between Lehigh Valley and Reading. Before being injured, he had converted five of seven save opportunities.
To make room for Alvarado on the 26-man roster, right-handed pitcher Connor Brogdon was optioned to Triple-A Lehigh Valley.
Brogdon's 28⅓ innings pitched ranked second among Phillies relievers, while his 27 appearances (one start) were tied for second on the club. Eighteen of those appearances were scoreless.
Information from The Associated Press contributed to this report.