Toews scored two goals and the Blackhawks (35-23-6) soared to their sixth successive win to move one point ahead of the Flames (33-24-9) and into fourth place in the Western Conference.
Chicago's current streak of victories includes wins against fellow conference contenders Nashville, Phoenix and Minnesota.
Blackhawks captain Toews has been pivotal in the surge, scoring six goals and making seven assists during his current seven-game point streak.
"We're scoring goals, we're making plays and we're putting the other team on their heels early in games," Toews said after registering his 25th goal of the season.
The Blackhawks jumped out to a 4-1 lead in the second period after goals from Toews, Michael Frolik and Brian Campbell.
Calgary fought back into the game in the third when Jarome Iginla scored his 28th of the season, while Rene Bourque added two goals in response to a lone strike from Chicago's Dave Bolland.
However, Chicago's Marian Hossa shot into an empty net in the final seconds to end any hopes of a dramatic fightback.
Flames goaltender Miikka Kiprusoff was coming off two consecutive shutout performances but he was pulled having allowed four goals to the Blackhawks through two periods.
"We were not good defensively. We gave up over 20 quality scoring chances against us and that's not good enough," said Calgary coach Brent Sutter.
"That's why I harp on what I do about defensive play. Defense wins hockey games and we get a lot of offensive opportunities when we do that."
Chicago netminder Corey Crawford finished with 21 saves.