Teixeira's early two-run blast -- coming after fans received a ceramic figurine in his likeness as a stadium giveaway -- forecast an ugly afternoon for lefty Ricky Romero, who was belted for six runs in six innings before the rains came.
The game was declared official and complete following a 58-minute delay, with the Yankees waiting to bat in the seventh inning. Earlier, lightning delayed the first pitch for 51 minutes.
Dewayne Wise also drove in two runs for the Yankees, who have won nine of their last 11 games. They've scored three runs or more in 42 straight games since May 30, joining the 1994 Indians (48 games) as the only teams to do so in the live ball era.
"We've swung the bats really well in the last couple weeks," Yankees manager Joe Girardi said. "I mean, really, really well. We've had some big outputs. We've jumped on people early. We've come from behind late. We've tacked on. It's probably about as good as we've played."
Robinson Cano extended his hitting streak to a career-high 21 games, the longest by a Yankee since Derek Jeter hit in 25 straight from Aug. 20 to Sept. 16, 2006. Nick Swisher logged a first-inning RBI single -- his 500th career hit as a Yankee -- and Andruw Jones also drove in a run.
"Our middle of the lineup feels consistent and has a chance to do some damage every day," Swisher said. "It's a lot of fun coming to the ballpark right now."
It was plenty of backing for Kuroda, who bounced back from a pair of rocky outings against the Red Sox and Angels for his first win in three efforts. He is undefeated in eight of nine starts since May 27.
"Especially when you have that kind of run support early in the game, you can be aggressive and try to go inside on righties and lefties, and that's what I did today," Kuroda said through an interpreter.
Kuroda showed excellent command of his splitter and slider in particular, limiting the Blue Jays to four hits. He walked none and struck out five in a 108-pitch outing, credited as his third career complete game.
"The Blue Jays are an aggressive team, and we just used their aggressiveness against them," catcher Russell Martin said. "The main thing is, you don't want to walk anybody. You want to make them earn it, so we pitched to contact."
The Yankees padded their lead in the middle innings off Romero. Wise stroked a ground-rule double in the fourth and added a sharp RBI single in the sixth, driving home Jayson Nix both times.
"You know you're going to get some pitches to hit," Wise said. "I know they'd rather face me than [Derek] Jeter and Curtis [Granderson]. You know you're going to get some fastballs, so you've just got to go in there, see it and hit it."
Romero has lost his last five starts for Toronto. He surrendered 12 hits, walking two and striking out two.
"I thought early on he was up in the zone quite a bit," Jays manager John Farrell said. "The way Kuroda was pitching, one run was going to hold up."
Toronto's star-crossed season received another scare in the third inning as third baseman Brett Lawrie tumbled into the camera well pursuing a Teixeira foul pop. Lawrie was taken for X-rays but was diagnosed with just a right calf contusion.
"I saw him go down and then I heard a loud crash," Teixeira said. "You really worry about a guy's head, neck and back. You never want to see somebody get hurt on a play, especially when you hit the ball."
The Yankees head for a seven-game West Coast trip vaulting off a 5-1 homestand, owning a healthy cushion in the American League East -- not that they see that as any invitation to slow down.
"No lead is big enough," Martin said. "I think we're just going to keep pushing and try to win as many games as possible. It'd be nice to win 100 games. We've just got to keep fighting, keep playing hard. If we do that, we'll be right where we need to be."