Connor scored on the power play and at even strength, and he set up a short-handed goal. He reached a career high 35 regular-season goals when he scored on the power play.
''The kid's scored 30 in the league every year so far,'' said Jets captain Blake Wheeler, who had two assists. ''I don't know how much blossoming he needs. We talked about it the other day and he had something like 70-something points and I don't know how many goals in college hockey. Those are freak-show numbers. I played college hockey and it's not easy to go out there and get two points a game, almost, in that league.
''I think, offensively, you saw that Kyle was a really gifted player around the net. What's transformed him into one of the more elite players in the league is his compete in and out of every shift. There aren't any lulls in Kyle's game anymore.''
Defenseman Tucker Poolman also scored - on an assist by Connor - for Winnipeg. Connor Hellebuyck made 25 saves.
''To compete, I think that's been the foundation for me as a player throughout my entire career and growing up,'' Connor said. ''I've always stressed that wherever I've played. I think it's just more of a consistency factor where I realized it's a grind the NHL game. It's an 82-game season, plus playoffs. The best players bring it every single night and that's what makes good players great.''
Defenseman Rasmus Ristolainen scored for Buffalo midway through the second period. Carter Hutton stopped 33 shots.
''Tough road trip, real tough,'' said Sabres defenseman Jake McCabe, who claimed the puck hopped over his stick on Winnipeg's first goal. ''I liked our start - at least for the first few shifts. Bad break there and we couldn't quite recover.
''It is quite unfathomable to be standing here after an 0-4 road trip like this, especially after how good we were playing going into it. We've just got to grab on to those small details and just keep working every single night and just keep growing this structure that (coach Ralph Krueger) has created for us here.''
Krueger credited his players for not giving up after going down 3-0 in the second period.
''I know we don't have quit in this group,'' he said.
It was the first of a three-game homestand for the Jets, who have won four consecutive games in their own arena and are 18-4-3 at home.
Ristolainen pulled Buffalo to within 3-1 midway through the second when he took a bad-angle shot that went in off Hellebuyck's left skate. Winger Kyle Okposo and center Johan Larsson were credited with assists.
With Ristolainen off for tripping, Connor had a power-play goal early in the second period to give Winnipeg a 3-0 lead. Left alone in front of Hutton, he converted a rebound of a shot by Patrik Laine. Wheeler also assisted.
The Jets had taken a 2-0 lead into the second period, thanks to a short-handed goal at the 15:05 mark. With center Nick Shore off for slashing, Poolman tipped a perfect pass from Connor past Hutton. Andrew Copp had started the play in his own end and was awarded and assist.
Connor had opened the scoring at 13:59 of the first. He converted a perfect pass from Wheeler on a 2-on-1 rush.
The Sabres buzzed Hellebuyck in the third period, especially after pulling their goalie with more than two minutes left. But they could not get the puck past Hellebuyck.
Connor had a couple of chances to score his third in the final frame, but was foiled by Hutton.
NOTES: Jets defenseman Josh Morrissey returned to action after missing four games with an upper-body injury. ... Forward Patrik Laine also returned after missing one game with a swollen left foot, the result of blocking a shot.
Sabres: Host Pittsburgh Penguins on Thursday.
Jets: Host Vegas Golden Knights on Friday.
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