Heading into the game, the Oilers had scored two goals in their previous 15 periods at home.
They scored three first-period goals, added three more in the second and another in the third to win their second consecutive game; they also earned a 4-2 win against the Calgary Flames on Saturday
"We played the right way," said Oilers forward David Perron, who had two goals and two assists. "More games like that are going to happen if we do that. I doubt it's going to be 7-0 every night. We did get some bounces tonight. It's nice to get a decisive win like that, compared to Calgary where I didn't feel we deserved it, but we found a way."
"The wins have been few and far between, and to have a game like that, especially at home, it's good for us. But, more importantly, it's good for our fans," Oilers coach Dallas Eakins said. "They've been suffering just as much as we have. It's nice to give them something to go home feeling good.
"One of the keys that we thought was going to be huge for us was breaking pucks out of our zone cleanly. We had a [heck] of a time with that against Calgary the other night. It wasn't our D-zone coverage; we couldn't break the puck out cleanly and we couldn't get out of our zone. But I thought we did a good job of that tonight."
Eberle opened the scoring 2:37 into game, depositing a rebound past Blue Jackets goaltender Sergei Bobrovsky.
Perron added to the lead on the power play at 12:01, getting to his own rebound in front. Smyth scored another power-play goal at 16:06, batting in a Sam Gagner centering feed.
The Oilers dominated the opening period, outshooting the Blue Jackets 15-3. They finished with 32 shots in the contest.
"I'm just really, really disappointed. We weren't ready to play the game," Blue Jackets coach Todd Richards said. "We weren't ready to battle or do the things necessary to win. There was no desperation and no urgency. I don't know … if we get too high on ourselves, you are going to have no success in this League. It was proven first-hand tonight -- if you aren't ready and willing to battle, this is what will happen to you.
"We weren't engaged at all. They were a desperate team and they got some ice to move in and you could see their confidence grow. The other thing is how we played the third period. We were just playing to run the clock out. As a coach, you watch certain things and how players respond in tough situations and we had guys that just wanted to get the game over with. I'm really disappointed with that."
Tuesday was the first time in five games the Blue Jackets failed to pick up at least a point. They've lost six straight at Rexall Place. They'll continue their five-game road trip Wednesday night against the Flames.
"That was disgusting," Blue Jackets forward Nick Foligno said. "We knew what kind of team they are and we played right into their hands. It is on everybody in this room. It is embarrassing. We handed them goals and gave them power plays and opportunities. It was really tough to be a part of this. I hope we have hit rock bottom here and understand that we are not a team that can play like this.
"It just didn't seem like we had that push-back, that answer. We gave them an easy night. They were able to skate around and do whatever they wanted. It's the wrong way to play. It was 7-0. It's obviously the wrong way to play."
Perron increased the Oilers lead at 8:30 of the second period, beating Bobrovsky from a tight angle along the goal line. Bobrovsky, the reigning Vezina Trophy winner, was pulled after the goal, finishing with 14 saves.
Curtis McElhinney replaced Bobrovsky, but he wasn't able to stop the onslaught.
Yakupov scored his fourth of the season and third in his past five games at 10:36, getting to a long rebound at the side of the net and firing it into an empty net.
Yakupov, the first pick at the 2012 NHL Draft, was going up against Ryan Murray, the second pick that summer, for the first time. The billing between No. 1 and No. 2 wasn't much of a contest since Murray, along with the rest of the Blue Jackets, had a rough night.
"We scored a pretty fast goal on the power play and 5-on-5 we played great in the defensive zone," Yakupov said. "That's how we have to play every game. My linemates helped me a lot tonight. That was awesome.
"We didn't give up anything defensively. I didn't think we played awesome for 60 minutes. But I thought defensively, we played well. We played man-on-man and we were winning battles. I think we showed the fans how we're capable of playing. We felt pretty comfortable out there."
Schultz, making his return to the lineup after missing eight games with a groin injury, scored the Oilers' sixth goal at 15:25 of the second period.
Hall closed out the scoring at 16:43 of the third, beating McElhinney on a breakaway.
The win was the Oilers' second at Rexall Place this season; they lost seven of their first eight at home. They host the Florida Panthers on Thursday.