Vrbata, who signed with Vancouver as a free agent this offseason after playing the previous five seasons with the Arizona Coyotes, has five points in three games playing with the Sedin brothers.
"It is about timing and being at the right place at the right time," Vrbata said. "If I do that, I know that they will find me."
Vrbata's second-period goal was his second game-winner of the season. He assisted on Daniel Sedin's empty-net goal with 15 seconds left in the game.
"I think it has helped [playing with Vrbata]," Daniel Sedin said. "He shoots a lot and that opens up a lot of things for us. He is a right-handed shot, and I think that gives our line an extra edge. He has been good."
It was the 30th career shutout for Miller, who signed with the Canucks in the summer after being traded from the Buffalo Sabres to the St. Louis Blues at the NHL Trade Deadline last March.
"It means a lot, you like to get the first [shutout] out of the way," Miller said. "It was an important game for us as well, to keep things moving along. We had a long break. You just try to make a difference where you can. It was one of those nights that I felt fortunate to keep it at zeros and then watch the guys get the lead. At the end of the night, we got rewarded. It was good."
Goaltender Ben Scrivens made 28 saves for the Oilers, who have not won a game this season. The loss extended Edmonton's season-opening losing streak (0-4-1) to five games, the worst start in franchise history.
"We have to find a way to come out on top," Scrivens said. "We played better in a lot of areas. We thought all of our lines played pretty well. They got one quality chance and buried it. We couldn't find a way to do the same with ours. Despite us playing better, we still have to find a way to push through and find a way. It's not a lot of condolence to play well and not win. We still have work to do."
The Canucks, who had been idle since defeating the Oilers 5-4 in Vancouver in a shootout Saturday, have won three straight to open the season, the first time Vancouver has done that since 1999.
After a scoreless first period, the Canucks and Oilers traded chances in the second. Miller was the busier of the two goaltenders in the period, making 15 saves. He kept the game scoreless with a number of big saves through the first half of the period.
Vrbata put the Canucks up 1-0 at 15:49 of the second, taking a cross-crease pass from Daniel Sedin and firing a shot up over Scrivens.
Henrik Sedin had taken the puck behind the net and dropped it to his brother, who swung out front and spotted Vrbata unattended at the far side of the net.
The Sedins each have six points.
Edmonton coach Dallas Eakins liked the Oilers' defensive effort and composure Friday.
"That was an even battle. I thought we had a lot more gamesmanship," Eakins said. "We just settled into the game. Our game plan was to firmly look after our end of the ice first and let the offense come when it comes.
"There are some games that we played this year where it's even and there is almost an anxiety on the bench where we have to go score right now. Or if we get down by a goal and we have to go get the goal back right away. That's not the case; you just have to settle in the game and let the opportunities present themselves."
Ryan Nugent-Hopkins came close to tying the game with a little more than seven minutes remaining in the third period, getting the puck in the slot on a 3-on-2 rush, but he fired his shot just wide.
"It's just frustrating that we didn't get a least a goal for [Scrivens] and for the effort that the guys put in," Oilers right wing David Perron said. "[All losses] feel the same, whether it's 8-1 or 2-0; for me, they all feel the same. We're trending in the right direction and we have to make sure we stick to it. We have to keep on cutting down on those chances in the slot, because it can go the other way pretty quickly and we have to stay on it."
The Canucks return home to host the Tampa Bay Lightning on Saturday. The Oilers continue their seven-game homestand Monday against the Lightning.