Canada (3-2) went on an 11-0 scoring run started by a pair of Cory Joseph free throws with 5:25 left in the fourth quarter.
Joseph accounted for six of the next eight points and a three-pointer by Brady Heslip at 2:25 cut the deficit to 60-57 before Venezuela called a timeout.
Tristan Thompson scored on an offensive rebound to make it a one-point game with two minutes to go, but that turned out to be Canada's final bucket.
David Cubillan hit a three-pointer at 1:36 and Venezuela's defence did the rest.
"I thought Venezuela did a really good job," said Canadian coach Jay Triano. "They're a very physical team, I think their average age is about 29 years old, and they have one way to play, and it's physical, and we were no match for their physicality."
Joseph led Canada with 14 points while Thompson added 12 points and a game-high 20 rebounds. Canada dominated the boards, out-rebounding their opponents 40-24, but were hapless from the arc where they shot just 4 of 25.
"Their defence stopped us from going where we wanted to go, and we had a hard time penetrating," said Triano.
Canada held Venezuela to 36 per cent shooting, "and you're supposed to win games like that, but when you don't score, that makes things tough," said Triano.
Nestor Colmenares scored 13 points and Cubillan added 12 for Venezuela (3-2), which moved ahead of Canada in the standings.
"This is what the international game is about, being in a foreign country with fans going crazy, and you're not going to get many calls," said Triano. "We've got to play through it."
The FIBA Americas Championship is a qualifying tournament for the 2014 FIBA Basketball World Cup in Spain. Canada next plays Dominican Republic on Saturday.