The sweep concluded a 10-game homestand that saw the Blue Jays (83-67) finish 6-4 and eliminate the bad vibrations from the Texas Rangers' four-game sweep of Toronto earlier in the week.
The Blue Jays hold an American League wild-card spot after the Rangers were swept by Cleveland and Seattle dropped the first two of its three-game set against the Los Angeles Dodgers.
Chapman's hit off reliever Garret Whitlock (5-5) gave the Blue Jays their sixth win in a row against Boston (74-76) after dropping the first seven games against their AL East rivals earlier in the season.
The game-winning hit scored Cavan Biggio, who reached base with a one-out single before 41,876 at Rogers Centre.
The Blue Jays led 1-0 after the second inning and 2-0 after Daulton Varsho's solo shot to right field with one out in the fifth.
Biggio reached safely in the second inning with an infield hit up the middle with one out. He advanced to third base on Chapman's double down the left-field line and scored on Kevin Kiermaier's sacrifice fly to left field.
Canadian starter Nick Pivetta was on the hook for both runs. But the Victoria righty lasted 6 1/3 innings, yielding only four hits with six strikeouts and a walk.
In the span between the Chapman double and Varsho homer, the 30-year-old Pivetta did not surrender a hit and retired nine of 10 Blue Jays.
Toronto lefty Hyun Jin Ryu pitched 4 2/3 innings of shutout ball, giving up six hits with two strikeouts and a pair of walks on 83 pitches.
He proved masterful in escaping jams. In the second and third innings, the Red Sox had runners on second and third with no outs but Ryu rallied for three consecutive outs on both occasions.
He also left a Red Sox runner at third base in the fourth with an inning-ending double play.
Boston left 12 runners on base and batted 1 for 14 with runners in scoring position.
Refsnyder scored on Reyes's single to centre.
This report by The Canadian Press was first published Sept. 17, 2023.
Tim Wharnsby, The Canadian Press