Hyman followed up with his second of the night, making it 6-3 at 15:18.
Ryan McLeod made it 7-3 at 16:58, wristing one past the stick of Luukkonen from the right face-off dot.
Connor Brown made it six straight goals, putting in a rebound with 10 seconds left for the 8-3 final.
The Oilers have outscored opponents 89-59 in the third period this season.
“We’re finding ways to get wins. I would still like to see a little bit more control of games,” said McDavid, the Edmonton captain. “I still think we are finding our game. It is nice that we are winning and producing wins, but I still think there is more there to be had, more urgency, which is a good thing.
“It’s that time of year when we need to ramp up and get ready to go. We are still playing for positioning and all that. There is still lots to be playing for.”
Peterka put Buffalo ahead 1-0 at 1:38 of the first period, taking a centering pass from Alex Tuch alone in front of the net and snapping it past the blocker of Skinner.
Rasmus Dahlin appeared to push it to 2-0 at 12:47, but the Oilers challenged for offside and video review determined Lukas Rousek preceded the puck into the zone.
Sabres defenseman Bowen Byram then fanned on a pass to the slot, causing Victor Olofsson to have to turn back to get it before spinning around and wristing it past Skinner for a 2-0 lead at 16:34.
The Oilers cut it to 2-1 on the power play at 18:55. Ryan Nugent-Hopkins took a pass from the blue line by Evan Bouchard, skated toward the net and dished it back to Draisaitl for a one-timer that squeaked in between the pad and the post.
Ekholm tied it 2-2 at 4:26 of the second period, entering the zone with a toe drag in front of Byram before shooting over Luukkonen’s glove from the left circle.
Peterka gave Buffalo a 3-2 lead at 16:56 with his second of the game, taking a centering pass from Connor Clifton and whiffing on the shot, only to see the puck slide under Skinner’s pad.
“I don’t think it’s frustration, I think I was still trying to score the whole time and obviously it kind of had to open up at some point,” Peterka said. “And they took advantage of almost every chance that we gave them.”
NOTES: McDavid became the fourth player in NHL history to have at least five four-assist games in a season. The others: Wayne Gretzky (eight times; most: 12 in 1985-86), Mario Lemieux (twice; most: seven in 1995-96) and Paul Coffey (five in 1988-89). … McDavid leads the NHL with 86 assists, putting him on pace for 105 this season. He can become the fourth player in NHL history to have 100 or more assists in a season; he would join Gretzky (11 times; most: 163 in 1985-86), Lemieux (114 in 1988-89) and Bobby Orr (102 in 1970-71). … The Oilers have an NHL-high 13 wins (13-3-1) when tied after to two periods and a League-high 20 wins when tied or trailing after two periods.