Lillard was 3 for 3 from the floor in the extra period as the Blazers escaped after blowing a 17-point lead in regulation.
"We didn't have a reason to be all riled up," Lillard said. "They played well getting back into the game. I think we were calm because we knew what we needed to do to win the game and we were able to get that done."
"The overtime we played well, especially defensively," Portland coach Terry Stotts said. "I was proud of the way we competed in overtime, made plays and got the win."
The Blazers made a season-high 15 3-pointers, finishing 15 for 32 from beyond the arc. Toronto made just three.
"It's tough when they're knocking down shots like that," Gay said. "No matter how much we rotate, move it around and switch, it's tough to play when a team has it going. I'm not happy they made shots, but I'm happy with the effort we put forth."
Portland's lost-distance accuracy wasn't a surprise to the Raptors coach Dwane Casey, who talked about Portland's potent offense before the game.
"[They're] one of the best offensive teams that we've seen," Casey said. "I think as far as scoring the basketball, averaging 103 points a game, they are a very explosive offensive team so we've got to be on point. We've got to guard the 3-point line."
Toronto was just 2 for 12 from the floor in overtime, while the Blazers continued to patiently move the ball and connect on 5-for-8 field goals.
Lillard wasn't thrilled with the fourth-quarter collapse, but was pleased with the way his team responded after it.
"We could have folded," Lillard said. "Once we got to overtime, on the bench we just said we need to get some stops, we need to execute and pull this game out. Then we went on the floor and we did it."
Batum hoped the young Blazers would use the game as a lesson.
"This wasn't the first time we have done it," Batum said. "Four or five times in a row we've had a good lead and had to close out the game and the other team came back. It paid off right now because we won in overtime and when you are up 15, 18 points with seven minutes to go, we have to close out the game."
The Trail Blazers visit Brooklyn on Monday. ... Kyle Lowry had 10 points and 10 assists for the Raptors.