The Jets scored first when Connor accepted a pass in front of the net from Blake Wheeler with 6:01 remaining in the first period.
Winnipeg took a 2-0 lead while on the penalty kill when Poolman tipped in a shot by Connor with 3:55 left in the opening period. The Sabres have allowed 11 shorthanded goals this season. Buffalo's power play ended the night 0-for-2.
Then, with Winnipeg on the power play after a too many men on the ice penalty by Buffalo, Connor tapped in a rebound for his second of the game at the 3:41 mark of the second period to go up 3-0.
The Sabres got on the board with 9:26 left in the second. Ristolainen put in work behind the Winnipeg net, cut around to the front and from a bad angle, threw a shot on goal. The puck went off Hellebuyck's leg and over the goal line.