Grilli was added to the roster Monday, a day after Texas acquired him in a trade from the Toronto Blue Jays.
The Rangers also reinstated left-handed pitcher Martin Perez from the 10-day disabled list to start the series opener against Boston. To make room on the 25-man roster, right-hander Keone Kela was put on the 10-day DL with right shoulder soreness and lefty Dario Alvarez was optioned to Triple-A Round Rock.
Texas has a majors-high 17 blown saves this season, matching their total from all of 2016. They have four in their last 10 games.
The 40-year-old Grilli is in his 15th major league season spent with nine teams. He made 26 appearances for the Blue Jays this year, and was previously in Texas for part of the 2009 season.
Toronto is sending Texas $991,803 on Sept. 30 as part of the trade. That covers a little more than half of the $1,740,437 that remained of his $3.5 million salary this year.