Bosh had 32 points and 10 rebounds, Bargnani added 21 points and the Raptors beat Grizzlies 103-82 on Friday night.
Bosh shot 11-for-13 from the field and 10-for-12 from the line to help Toronto pull away in the fourth quarter and extend its home winning streak to a season-high three games.
That streak will be tested when Toronto hosts Boston on Sunday, the first of back-to-back games against the division-leading Celtics.
"We won the games we felt we were supposed to win," Bosh said, referring to victories over Washington, Orlando and Houston. "We're just trying to keep everything moving. We know the schedule is going to get a little bit more challenging from here on out."
Toronto coach Jay Triano said Bosh, who topped 30 points for the tenth time this season, was "as solid as he has been in a long, long time with great energy at both ends of the floor."
Bargnani is averaging 21.7 points as a starter in the past six games in place of the injured Jermaine O'Neal and has made 19 3-pointers in that span. He finished 3-for-4 from behind the arc Friday.
"We know one thing: Andrea will shoot it when he's open," Bosh said. "He made good shots, the defense didn't rotate fast enough and he made them pay for it."
Rudy Gay scored 22 points for Memphis, which has lost 11 of 13. The Grizzlies have been held under 90 five times in the past six games.
"Bosh really took it to us," Gay said. "He forced us to try and scramble out there and he knocked down shots."
Hakim Warrick scored 18 and Kyle Lowry added 12 for Memphis, which has lost five straight on the road. The Grizzlies are 2-15 away from home.
"They did a really good job of taking us from what we were comfortable with and making us go to our third and fourth options," Warrick said.
Memphis rookie O.J. Mayo, the team's leading scorer coming in, was forced to the bench after he was kneed in the left hip when he collided with Toronto's Jamario Moon while going up for a defensive rebound in the first. He finished with 11 points in 33 minutes, shooting 4-for-14.
"It was pretty much nagging me throughout the game," Mayo said. "It probably would have been best to just sit out but I tried to fight through it. That side was pretty sore. You really don't know how much you need it until it happens to be injured. It kind of kept me back a little bit."
Memphis shot 12-for-34 in the second half and was outscored 56-38 after the break.
"We can't let our offense affect our defense and I think sometimes we do," Lowry said. "It's definitely hard but we've got a lot more games to go. We've got to bounce back. We've got a couple of days of practice coming up ahead and we've just got to get better."
Jason Kapono scored 11 points and Will Solomon had 10 points and nine assists for Toronto, which has won four straight over Memphis after losing the previous eight meetings.
Toronto was without O'Neal (right knee) for the sixth consecutive game, while guard Jose Calderon (right hamstring) missed his fourth straight. Moon returned after missing Wednesday's win at Washington to be with his wife while she gave birth to the couple's first child, a daughter.
Memphis coach Marc Iavaroni said he "wouldn't rule out" re-signing forward Darius Miles, who was waived by the team Tuesday. If Miles plays in two more games this season, his former team, Portland, would be on the hook for $18 million over the next two years, the amount remaining on Miles' contract, which would count against Portland's salary cap and force the team to pay luxury tax. ... Memphis never led by more than one point. ... Toronto shot a season-high 55.6 percent, going 40-for-72.