Davis hit a pair of solo homers in the second and fourth innings off Blue Jays starter Carlos Villanueva, the first homer hitting Eutaw Street.
Davis then crushed a two-run homer in the sixth off reliever Steve Delabar to give the Orioles a 5-1 lead, igniting the announced crowd of 25,754 at Camden Yards.
Davis, who now has 23 homers on the season, came out for a curtain call after his third homer.
Davis also became just the fourth Orioles player to hit three homers at Camden Yards, joining Markakis, Albert Belle (1999) and Roberto Alomar (1997).
Three other Orioles players had three-homer games at Memorial Stadium: Randy Milligan in 1990, Juan Beniquez in 1986 and Bobby Grich in 1974.