Chapman (1-0) allowed one hit and struck out one over a scoreless inning to pick up the win over Texas on Thursday.
Chapman, who was named Boston's primary closer earlier this week, entered a 2-2 game in the eighth inning. It appears the decision to use the closer in the eighth was because the Rangers had the top of the order due up. Chapman worked around a one-out, broken-bat single, throwing seven strikes among his 11 pitches. After the Red Sox took a 5-2 lead in the top of the ninth, Justin Slaten shut the door for Boston.