Marian Hossa also scored in the second period for Chicago and Saad added an empty netter late. Corey Crawford made 29 saves as the Blackhawks grabbed sole possession of first in the Central Division.
Chicago scored four times on five shots in a span of 7:31 in the second to rally from two goals down and snap a four-game winless streak (0-2-2). The Blackhawks bounced back after falling 5-4 to Calgary in overtime a night earlier and are now 10-1-3 in the second game of back to backs this season.
The victory was Blackhawks coach Joel Quenneville's 693rd, moving him past Dick Irvin into sole possession of third place on the all-time NHL coaching wins list.
Chris Higgins and Tom Sestito scored for Vancouver, which lost its second straight. Roberto Luongo stopped 36 shots.
Trailing 2-0, the Blackhawks got on the scoreboard with a power-play goal as Hossa completed a tic-tac-toe passing sequence for his 23rd of the season at 6:30 of the second period.
Chicago tied the score 3:39 later when Saad scored his 15th of the season on a sweet deflection off a point shot from Sheldon Brookbank.
Toews then swatted a losse puck in the crease past Luongo for his 18th at 10:47 to put the Blackhawks ahead, and Sharp made it 4-0 with his 27th with 5:33 remaining.
Vancouver had a chance to get back in the game later in the period, but the league's 29th-ranked power play, which entered the night on a dismal 2-for-36 run, failed to generate anything.
Needing a big third period, the Canucks couldn't get anything past Crawford on another man advantage midway through the period as Toews sprawled on the goal-line to keep Higgins' effort out.
Saad then sealed the win with 38 seconds left into an empty net.
Fans at Rogers Arena were just settling into their seats after the national anthems when Higgins opened the scoring just 16 seconds in. Canucks forward Ryan Kesler shovelled a puck towards the Chicago goal that Higgins sent between Crawford's legs for his 15th goal of the season and third in the four games.
The Blackhawks were leading 13-3 on shots before the Canucks pushed back late in the period. Kesler had three straight chances in front of Crawford, with the final one going off the goalie's mask but staying out.
Crawford then made a huge toe save on Canucks forward Brad Richardson in front to keep the score 1-0 after 20 minutes.
Sestito doubled the Canucks' lead at 2:44 of the second with his fifth of the season.
NOTES: The Canucks head on a five-game road trip that will take them to Winnipeg, Detroit, Boston, Montreal and Toronto. Vancouver's next home game is after the Olympics, on Feb. 26 against St. Louis Blues. ... The Blackhawks continue their six-game pre-Olympic road trip on Saturday at San Jose.