Graovac scored at 13:09 of the first period when he gathered a loose puck in front and slid it past Talbot.
Zucker scored with 3.6 seconds left to put Minnesota up 2-0.
Parise scored at 4:15 of the second period, converting a pass in front from Jason Pominville.
Larsson scored on a point shot at 11:08. The puck deflected in front and skipped past Kuemper to make it 3-1.
Graovac's second goal ended Talbot's night. He capitalized on a turnover deep in the Oilers zone to put Minnesota up 4-1. It was Graovac's first two-goal game in the NHL.
"It feels good," Graovac said. "Chipping in any way you can, whether it's a faceoff or being good defensively or giving momentum to the next line, that's our job as the fourth line. That just helps everybody."
Draisaitl scored on the power play at 16:47 when he converted a pass from Milan Lucic in the slot to make it 4-2.
Stewart made it 5-2 when he took a pass coming out of the penalty box, kept the puck on a 2-on-1 rush and shot through Brossoit's pads.
Pominville had a goal waved off at 16:49 after he was ruled to have batted the puck in the net off a scramble in front.
"It was catastrophic mistakes, often just by individuals, that really caused us problems," Oilers coach Todd McLellan said. "We were flat, we didn't execute well, we weren't good around the net. They were the better team. We got what we deserved."
