Saad snapped a shot past Corey Price from the low edge of the right circle for the winner. Patrick Kane shot from the top of the slot and Canadiens defenceman Andrei Markov couldn't handle the puck.
Chicago's Jonathan Toews scored a power-play goal early in the third to tie it at 3. Michal Rozsival and Ben Smith connected at even strength as the Blackhawks won for the eighth time in nine games.
Montreal's Brendan Gallagher scored and set up 40-year-old Sergei Gonchar's first goal in nearly a year. P.K. Subban added a power-play goal for the Canadiens, who have lost two straight and are 1-4-1 in their last six.
It was the second and final regular-season contest between the Original Six rivals. The Blackhawks won 5-0 at Montreal on Nov. 4.
Antti Raanta made 38 saves as Blackhawks No. 1 goalie Corey Crawford sat out his second game with a foot injury, sustained while leaving a concert.
Price blocked 32 shots.
Gonchar, acquired from Dallas on Nov. 11, scored his first goal with the Canadiens and first since Jan. 25, a span of 44 games.
Rozsival, a defenceman, opened the scoring 2:13 in with his first goal of the season to cap a 3-on-2 rush.
Raanta's pad save denied Brandon Prust on a breakaway midway through the first to maintain the lead, then Smith made it 2-0 with 1:44 left in the period.
Smith's shot from right wing hit traffic in front and bounced around just beyond the crease, but Smith plowed to the net and chipped in the loose puck.
Gallagher responded just 26 seconds later to make it 2-1 and nip Chicago's momentum when he one-timed a rising shot from right hash marks into the upper left corner of the net.
Gonchar tied it at 2 at 7:58 of an up-tempo second period.
Subban put Montreal ahead 3-2 with 2:38 left in the second, just 13 seconds into a Canadiens power play.
With Subban off for hooking, Toews' power-play tap-in at 4:18 of the third made it 3-all.
NOTES: Montreal C Lars Eller sustained an upper-body injury in the first period and didn't return. ... Blackhawks F Patrick Sharp missed his 13th game (knee) on Friday, but could rejoin the team during a four-game road trip that starts Saturday in Nashville. Chicago has been on a roll without the 32-year-old winger, who led the team in goals (34) and points (78) last season. "I'm just trying to get myself back into game shape and jump right in," Sharp said. He was injured on Nov. 4 in Montreal. ... The Blackhawks honoured Canadiens great Jean Beliveau, who died on Tuesday, with a pregame moment of silence. ... The crowd or 22,087 was the Blackhawks' largest this season.