"The puck found a way to me in front and it was an easy tap-in," said Saad, who broke a six-game goalless streak.
Chicago, which was shut out in its previous two games, defeated Winnipeg for the first time in four games. The Jets have lost six in a row (0-4-2).
Kane stopped Chicago's scoreless streak at 149:25 with a goal 2:50 into the second period.
"It was tough to generate [opportunities]," Kane said. "[The win is] big. I think it was a big game against that team and also a big game for our team. It was one of those games where you had to stay patient, keep yourself in the game and just wait for your opportunities."
The Blackhawks (32-18-2), who are 9-2 in overtime, moved four points ahead of the Jets (26-18-10) in the Central Division with two games in hand. Chicago finishes its season-high seven-game road trip Sunday at the St. Louis Blues before playing eight consecutive games at United Center. A regulation win Sunday would move the Blackhawks within four points of the Blues and Nashville Predators.
The win was No. 300 for coach Joel Quenneville with the Blackhawks (300-145-61). He has the best winning percentage in Blackhawks history and ranks third all-time among NHL coaches with 709 wins (709-410-178).
"I'm fortunate, very fortunate to have had great players," said Quenneville, who started with Chicago in the 2008-09 season and has won two Stanley Cup championships.
The Jets began Friday with the news that left wing Evander Kane is out for the rest of the season. The 23-year-old, who had 10 goals in 37 games, will have surgery on his left shoulder and be sidelined 4-6 months. Kane was scratched Tuesday against the Vancouver Canucks, a move Jets coach Paul Maurice called a coach's decision.
Winnipeg holds the first wild card spot into the Stanley Cup Playoffs from the Western Conference and leads Vancouver, the second wild-card team, by three points. Vancouver has four games in hand on Winnipeg, which is in a stretch of seven consecutive games against Western Conference teams.
Maurice said he saw improvement from the Jets, who allowed 23 goals in the prior five games.
"We weren't happy with where we were coming out of the [All-Star] break with those games, but we're happy with our [past] two [games]," Maurice said. "We'd like to have won them. It goes without saying, but we can understand more of what we saw, so now we have a better comfort level of getting back to our game."
Hutchinson and Blackhawks goaltender Corey Crawford each made 20 saves.
"That was a pretty physical team," Crawford said. "We just had to be smart with the puck, especially at the end of the third period. We made the right plays when we had to. It's just a big win for us right now."
The Jets took a 1-0 lead 4:17 into the game when Mark Scheifele drove the net before snapping a shot over Crawford's left glove. Scheifele's eighth goal ended a 10-game drought and was his second in the past 22 games.
Chicago tied the game when Kane broke loose at the Winnipeg blue line and backhanded a shot over Hutchinson for his 26th goal. With two points, Kane tied Philadelphia Flyers forward Jakub Voracek for the NHL lead (58).
Kane scored Chicago's prior goal at 13:25 of the third period of a 4-1 win at the Anaheim Ducks on Jan. 30. The Blackhawks lost to the Minnesota Wild 3-0 on Tuesday and to the San Jose Sharks 2-0 on Jan. 31.
Hutchinson was 3-0-0 against Chicago this season with a 1.00 goals-against average and .971 save percentage.
Quenneville admitted the goal was needed, given Hutchinson's play in the series and the Blackhawks' recent scoring problems.
"[Kane] was dangerous," Quenneville said. "He made several plays tonight that were kind of characteristic of how he has been all [season]. Very dangerous, but certainly you start thinking about it when you don't score for seven periods, you're on the road, a tough building, and [against] a team we haven't had any success scoring against all season. It was much-needed.
"It was almost like a playoff game. It had that sense in the building and the same way on the ice."
Crawford also compared it to a playoff game.
"I think the other games against [Winnipeg] had that type of feel," he said. "They just play that type of game. Everyone on their side plays physically, and it just seems like there is no room."
Winnipeg often steered the game toward the physical, confrontational style that has marked its transition since Maurice took over from Claude Noel in January 2014. The Jets outhit the Blackhawks 41-16.
"It was hard for any team to get traction," Maurice said. "So I think because of the way the game was played, we're not 100 percent responsible for the way the game is played. [Each] team [has] a [really] big impact. [Each] team [was] kind of doing the exact same things.
"There were just a lot of pucks along the walls. It looked like they were trying to bat a lot of pucks. [Each] team [was not] sure of which way the puck was going on a lot of the confrontations, and it slowed the game down."
Scheifele said he liked what he saw from the Jets.
"A big, strong, fast, physical team," he said. "That's the way we want to play. That's Winnipeg Jets hockey, and we definitely showed a lot of that."