Nugent-Hopkins scored to end the rally and make it 7-5 at 18:59.
"We have to find a way to put teams away," he said. "There hasn't been a ton of games where we've been up, especially that much this season, but we still need to do a good job. Bottom line is we did come away with the victory, so you can't dwell on it too much. But we can learn a lot from that game."
Puljujarvi scored at 10:29 of the first period, and extended Edmonton's lead to 2-0 at 14:33 when Eric Gryba's point shot deflected off his shin pad after going through the hole in Mark Giordano's skate blade.
Frolik made it 2-1 with a shorthanded goal at 16:21. Khaira gave the Oilers a 3-1 lead when at 17:44.
Letestu put Edmonton up 4-1 on a shorthanded breakaway at 3:40 of the second period. Lucic deflected Gryba's point shot with 21.2 seconds left in the period to make it 5-1.
"What concerns me is with this group, on the mental side of the game, is that flight, fight or freeze mentality," Gulutzan said. "We seem to freeze a bit until something good happens and then we can start to move. That is something we've got to address."