Grichuk would account for three of the Toronto runs while Teoscar Hernandez also chipped in with a homer, his 18th on the year.
Toronto went ahead 4-2 with runs in the second and third frames, but the Red Sox tied things up in the fourth on a home run by Martinez - the first Borucki has surrendered in the big leagues over 47 1/3 innings - and back-to-back two-out singles from Nunez and Brock Holt.
Betts hit a no-doubt home run to left in the ninth inning off Toronto closer Ken Giles to record the cycle.
He's hit his first career walk-off homer, clubbed his 100 career home run, and he's now leading the Majors in batting average.
In improving to 2-2 in his rookie season, Borucki served up nine hits over his five innings - but held the Red Sox to a respectable four runs. They overwhelmed the Woe's in a 19-12 victory that saw them erase an 8-3 deficit, overcome a back-to-earth start from Nathan Eovaldi, and pile on 14 runs between the sixth and eighth innings. And they're hot right now.
"If he's on though, he'll be tough", Gibbons predicted before the game about Borucki's coming Red Sox challenge.
Betts, 25, is in the midst of an MVP-caliber season. He hit a two-run single to give Boston a 2-0 lead.
The 2016 A.L. Cy Young Award victor was uncharacteristically off, issuing two walks to the first two batters he faced.
In the fifth, Boston's Martinez hit a solo homer to cut Toronto's lead to 4-3. Pannone served an 80-game performance enhancing drug suspension earlier this season. RHP Dylan Bundy (7-10, 4.38) starts for the Orioles.
Red Sox: LHP Eduardo Rodriguez (right ankle sprain) threw effectively in a simulated game, with positive results.
Red Sox: David Price (11-6, 3.93 ERA) will work the first game of a split doubleheader on Saturday. Estrada allowed one run in seven innings against Seattle in his previous outing, snapping a four-start winless streak.