Connor McDavid had a goal and an assist, and Mike Smith made 33 saves for Edmonton (16-9-3), which has lost two straight.
Each team will play again tomorrow at Rogers Arena.
"It was just not good enough all over, special teams, it was just not good enough," McDavid said. "I thought we did a good job of battling back and we even had a push there in the second where we could have made it 3-2, and just one little mistake and it's in the back of our net and they're up 3-2. And they're a team you can't play against from behind. You have to try and get the lead on these guys because they're pretty good at shutting it down."
Tyler Graovac scored on the power play at 3:31 of the first period to give Vancouver a 1-0 lead. Play continued until the Situation Room informed the off-ice officials to sound the in-arena horn at 3:49, when it confirmed that Graovac's shot completely crossed the goal line.
Pearson scored shorthanded on a 2-on-1 rush at 13:32 to make it 2-0, but McDavid took a pass from Ethan Bear in the right circle and scored blocker side to cut it to 2-1 at 14:14.
"We needed that one," Pearson said. "After the way Pittsburgh went (8-6 loss on Wednesday), to get the lead tonight, hold it and keep on pushing, was a big step."
Zack Kassian tied it 2-2 at 5:05 of the second period. After McDavid poked the puck away from Canucks forward J.T. Miller, Kassian skated in on a 3-on-2, waited and scored from the top of the right circle.
Pearson scored on a rebound at 13:47 to give Vancouver a 3-2 lead, and Loui Eriksson scored his first of the season on a one-timer to make it 4-2 at 18:04.
"It wasn't a very good first period and it felt like we were coming, we were getting at least some zone time in the second period," Oilers coach Dave Tippett said. "But then, ultimately, if you give up five you can't win in this League. We're giving up too many goals right now and it's costing us. We're just playing a little loose right now, looser than I'd like, and chasing the game and we don't have the same commitment to defending. We have to have the same mindset to defend a little better."
Josh Leivo scored at 1:21 of the third period on a wraparound for the 5-2 final.
"It's a big win for us, especially to get that win against a good team in their own building is big for us," Horvat said. "Now we have to carry that momentum into tomorrow night. It was a great start and that helped set up the rest of the game, and [Markstrom] made unbelievable saves and kept us in it."
