With the win, the Oilers kept pace in the Western Conference playoff race, sitting in a tie with Columbus, one point back of the eighth-place St. Louis Blues.
"We had an optimal start again," Oilers coach Ralph Krueger said. "When you take advantage of early opportunities, you put yourself in the driver's seat."
Krueger said one of the things he is most pleased with is that his team wasn't satisfied with the way they played, despite the big win over their provincial rivals.
"I thought it was good that we didn't feel good about the way we played all the way through the game today," he said. "It's a sign of the maturity of the group. The wins and losses are critical right now, but how we play and maintain this run is important. We feel confident right now and just want to keep nudging as a group."
Ryan Jones agreed that his team allowed themselves to gear down after the early lead.
"That definitely wasn't the best hockey we've played in this stretch, but we did what it took to win," he said. "Devan Dubnyk stood on his head."
Dubnyk had 33 saves for the Oilers.
Brian McGratton scored for the Flames, who saw defenseman Jay Bouwmeester traded to St. Louis shortly before the game.
"We gave them some odd-man rushes and if you get caught standing around you are going to pay," Flames center Matt Stajan said. "They caught us napping for those first two goals and we were chasing them for the rest of the night."
Stajan said the trade before the game and the one the week before that sent captain Jarome Iginla to Pittsburgh were tough to take, but have to be overcome.
"That's twice in the last week that has happened and you can say all you want about it, but as players we can't make excuses," he said. "We have to come out and play with more grit. Especially against our provincial rivals."
Flames coach Bob Hartley said the trade deadline can take its toll on players when they are in the situation Calgary is in.
"This is the time of the year where there is speculation and rumors, but there are still games going on," he said.
The Flames have lost two in a row and six of their past eight games.
Edmonton struck first just before the four-minute mark to start the opening period as Hall spotted Schultz creeping in from the point and fed him the puck in the slot where the rookie was able to beat Calgary goalie Miikka Kiprusoff for his sixth of the season.
The pair did it again midway through the first as Schultz picked off a pass in the Calgary zone and sent it to Hall in front. Hall was able to stop Kiprusoff with a deft move and then lift in a backhand for his fourth goal in the past two games.
Edmonton scored on both of its first two shots in the game, similar to what happened in its 4-0 blanking of Vancouver on Saturday.
The Oilers went up 3-0 with 3 1/2 minutes to play in the first as Jones beat Cory Sarich to a puck along the boards and muscled a one-handed backhand shot that got through Kiprusoff.
The veteran goalie was pulled in favor of backup Joey MacDonald after allowing three goals on six shots.
The game slowed in the scoreless second period with the best chances belonging to the Flames, however Dubnyk was able to come up with a pair of big saves on a tip by Curtis Glencross and a nice move by McGratton.
The Oilers put the game away midway through the third as MacDonald got a piece of a Yakupov shot from the slot, only to see it dribble in behind him. It was the first goal in 17 games and seventh on the season for the 2012 first-overall draft pick.
Calgary spoiled Dubnyk's hopes of earning a second consecutive shutout with just 1:32 left as McGrattan scored.
The two teams play again in Calgary on Wednesday.
It was the second of four games between the two provincial rivals this season. Calgary took the first meeting 4-3 on Jan. 26. ... The Flames have had the better of the matches in recent years, and came into the game having won 10 of their past 12 meetings over the Oilers ... The latest trade came on the heels of last week's trade to Pittsburgh of captain Jarome Iginla. ... The Oilers also made news earlier in the day with the re-signing of defenseman Ladislav Smid to a four-year deal worth $3.5 million per season. ... The Oilers have recalled center Anton Lander from AHL Oklahoma City with Eric Belanger out with a groin injury. Lander did not suit up in the game. ... Calgary's top goal scorers, Glencross and Michael Cammalleri, came into the game having managed just five of their combined 25 goals on the road.
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EDMONTON, CANADA - APRIL 1 : Mikka Kiprusoff #34 of the Calgary Flames warms up prior to a game against the...