The Red Sox (75-76) entered Monday hitting .190 with runners in scoring position in September, but they came through in key situations to break a four-game skid.
Rafael Devers, Bobby Dalbec and Luis Urias each logged multiple hits and scored a run. Urias also hit a game-tying single in the fifth.
Kutter Crawford struck out seven over six innings of two-run ball, and Josh Winckowski (4-2) worked around two walks to strike out the side in his inning of work to earn the win.
Garrett Whitlock followed, and Chris Martin closed out his second save and 19th consecutive scoreless appearance.
Texas (82-68) logged two hits against Crawford in its two run-scoring innings and totaled only five in the game. Marcus Semien was 2-for-4 with both RBIs.
The Red Sox jumped on Texas reliever Will Smith (2-7) in the eighth. Urias walked and Connor Wong cranked a double into the left-field corner to set up the deciding three-run inning.
Two batters later, Devers was intentionally walked to load the bases, and Refsnyder made Texas pay with a two-run single that flipped the score. Adam Duvall's sacrifice fly added an insurance run.
Rangers third baseman Josh Jung (left thumb fracture) and right fielder Adolis Garcia (right patellar tendon strain) went 1-for-4 and 0-for-3, respectively, in their first game back from the injured list.
Left-handed starter Jordan Montgomery allowed one run on five hits and fanned eight in seven innings.
The Rangers got off to a good start as Semien sent Crawford's first pitch of the ballgame out to left field.
Crawford allowed another hit — a one-out single by Nathaniel Lowe — in the first before retiring the Texas side in order in each of the next four innings. He needed just four pitches to get through the fourth.
Dalbec's one-out double off the right-field wall and a Urias single up the middle plated the tying run in the fifth.
Texas' hitless run against Crawford ended in the sixth when Evan Carter laced a leadoff triple to right-center and scored immediately following Semien's base hit to center.
—Field Level Media