Toronto's Raimel Tapia hit an inside-the-park grand slam after Boston's Jarren Duran lost the ball in the lights and didn't try to get it.
The BlueJays broke the franchise record for runs in a game with 25 in the fifth and went on to win 28-5.
There are two inside-the-park slams in Toronto's history. It was part of a seven-runnning.
In the third, Tapia hit a two-out fly ball to center against Davis.
He put up his hands after taking a couple steps back. The fans groaned when the ball came down.
Left fielder Alex Verdugo slid to scoop the ball and threw it to the infield as Duran walked slowly towards the ball. The relay home was not close to nabbing Tapia, who picked up speed when he realized he had lost the ball.
The 25-year-old is in his second major league season.
The club scoring record was broken on June 26, 1978, when the BlueJays beat Baltimore 24-10). John Mayberry entered as a pinch-hitter and hit two homers and drove in seven.
Boston had a record for runs allowed in a loss to Cleveland.
Junior Felix had an inside-the-park slam in Boston in 1989.
The BlueJays entered the day with a two-game lead over Boston for the last wild-card spot in the American League.