Aaron Johnson and Troy Brouwer also scored for Chicago (7-3-3), off to its best start since 2001-02 - the last time it made the playoffs.
Toews' goal was his first in 13 games this season and came on his 41st shot. He had 24 goals and 30 assists last season in 64 games as a rookie.
Toews, who had five of Chicago's 27 shots against Calgary's Miikka Kiprusoff on Sunday, scored early in the third period to give the Blackhawks a 4-1 lead. Versteeg connected 28 seconds later to put the game out of reach.
After Kiprusoff robbed Toews on two prime chances, the former North Dakota star scored on a shot that trickled through Kiprusoff's pads.
"I thought is was another shot in the chest like in the second period when I had the break," Toews said. "It had to be a goal like that, where it wasn't going to be pretty. It went in. It's a confidence boost."
The 20-year-old Toews is in his first season as the Blackhawks' captain.
"I was trying hard and forcing a little bit," Toews said.
After killing four penalties in the first period - including a double-minor to Havlat - and eight overall, Chicago coasted to the win.
The Blackhawks, whose special teams have improved drastically, were 2-for-7 with the advantage,
"The penalty killers did a great job at the start and end of the game," Chicago coach Joel Quenneville said. "It was a very solid game."
Blackhawks goalie Cristobal Huet made 22 saves, allowing only Dustin Boyd's second-period goal. Kiprusoff stopped 21 shots for Calgary, which lost its second straight game and fourth in its last five.
The Flames skated with several flu-stricken players in their third game in four nights. Kiprusoff made several close-in saves and twice was beaten by shots that hit the post.
"We have some guys with the flu, but we don't want to use that as an excuse," Calgary coach Mike Keenan said.
Calgary captain Jarome Iginla agreed.
"Our power play was bad," Iginla said. "We wanted to jump on them early and didn't do it. They got better as the game went on."
Havlat's power-play goal midway through the first period opened the scoring. After the Blackhawks created a 2-on-1 advantage in front of the net, Havlat ripped in Versteeg's feed from across the crease.
Johnson scored on a screened drive from the left point with just under a minute left in the first to make it 2-0.
Kane's goal midway through the second made it 3-0. He lifted in a shot from the right side of the net after taking Havlat's backhand pass from across the crease.
Boyd cut it to 3-1 with 1:21 left in the second when his weak backhand attempt from the right side of the net bounded in off Huet's left pad.
Toews and Versteeg scored goals 28 seconds apart early in the third.
Toews' shot from the slot hit trickled in between Kiprusoff's pads 54 second into the third. Versteeg ripped in a screened shot from the slot at 1:22.
Brouwer's power-play goal with 4:09 left in the third completed the scoring.
Notes: Calgary C Matthew Lombardi missed his ninth game because of a shoulder injury. ... Chicago D Brent Sopel sat out the game because of an undisclosed injury. ... Linesman Andy McElman was struck by a puck late in the third period, but remained in the game after being attended to by Chicago trainer Mike Gapski. ... The Blackhawks played their first game following a five-day break.