Derek Roy had a goal and two assists as the Oilers came away with a 5-2 victory over the Chicago Blackhawks on Friday.
Benoit Pouliot, Jeff Petry, Nail Yakupov and Taylor Hall also scored for the Oilers (10-23-9) who have gone 3-1-2 under Nelson since he took over sole coaching responsibilities when G.M. Craig MacTavish moved back upstairs after joining Nelson for five games in the wake of the firing of Dallas Eakins.
The Oilers had lost 20 of their previous 21 games before showing some recent signs of life.
"It's fun to win," Hall said. "It does make you forget about what place you are in the standings for a couple of days. We need that, we need to be a relaxed group. For us, winning helps out a lot with that.
"We're starting to gel a lot as a team. When we get down, we come together, we don't try to do too much individually, we're starting to play like that and it's helping out a lot. It's a nice little stretch for us. A win is a win, no matter where it is in the season. And when you're winning against a team like Chicago it's even better."
"That's how we have to play every game," added Yakupov. "That was really a team game tonight. It was really exciting. We started to play the right way."
The Oilers twice scored quickly after allowing a goal, something Nelson said was a good sign that there is still some fight in the squad.
"It was a great sign that we could bounce back right away," he said. "That's good to see, hopefully that continues and we keep on maturing in that direction. Once they scored, our guys stuck with it and got rewarded."
Brandon Saad had both goals for the Blackhawks (27-13-2), who have lost two of their past three games.
"They played a good game, but we had all the chances we needed to win this game tonight," said Blackhawks goalie Antti Raanta. "I've played better games myself.
"The game winning-goal, the third one, if you let that kind of bad rebound right to a guy's stick, you have to recover and make the save. You can't let in that kind of goal. We lost the game almost because of me, so it is a bad feeling."
The Blackhawks were coming off a tough trip after playing the Wild in Minnesota on Thursday night, but Saad said they can't use that as an excuse.
"It's tough, but there are no excuses," he said. "It is part of the NHL and the schedule. We can't blame it on that. We got outworked tonight. It was a big game for us and a tough loss.
"We're not happy with our last two performances."
The Blackhawks started the scoring seven-and-a-half minutes into the first period as Oilers goalie Ben Scrivens was able to make an initial stop on Chicago forward Jonathan Toews, but the Edmonton defence let Saad skate in unmarked to deposit the rebound into the net for his 11th goal of the season.
Edmonton got that goal back just over a minute later as Pouliot tucked a puck past Raanta during a scramble in front of the Blackhawks net.
The Oilers went up 2-1 on the power play with six-and-a-half minutes left to play in the opening frame. Teddy Purcell fed a puck in front of the Chicago net and Roy came racing in to deflect it past Raanta.
Chicago tied the game six minutes into the second period as Oilers defender Nikita Nikitin blew a tire, allowing a two-on-one. Marian Hossa elected to shoot on the play and the rebound came directly to Saad, who scored his second goal of the game.
Edmonton came flying back to regain the lead only 46 seconds later as Petry joined the rush and slipped the rebound from a Yakupov shot through Raanta's legs to make it 3-2.
Scrivens kept his team in the lead with five minutes left in the second period as he made a huge stop on Andrew Shaw on the doorstep.
The Oilers were able to clamp down on defence and limit the Blackhawks' chances in the third until Yakupov was able to put the game away, coming in with Hall on a two-on-none opportunity and electing to shoot himself, beating Raanta on the backhand with three minutes remaining. It was Yakupov's first goal in 15 games.
Hall added an empty-netter shortly afterwards.
Scrivens recorded 19 saves in the win.
Both teams return to the ice on Sunday as the Blackhawks return to Chicago to face the Wild and the Oilers finish off a four-game homestand against the Florida Panthers.
Notes: It was the second of three games between the Oilers and Hawks this season. Chicago dominated the first contest with a 7-1 win in Edmonton in November. The Blackhawks entered the game having won five in a row over Edmonton, dating to the 2012-13 season… Chicago backup goalie Antti Raanta got the nod in net after watching Corey Crawford make the previous seven starts for the team… There were some obvious statistical differences between the two teams entering the game, the most glaring being goal differential. The Blackhawks were +35 in goal differential (123-88), while Edmonton was -47 (89-136)… Remaining out with injuries for Chicago were Trevor Van Riemsdyk (patella fracture) and Kris Versteeg (upper body), while Edmonton was without the services of Tyler Pitlick (lacerated spleen)… Derek Roy became just the fifth Oiler to have a three-point game this season. Chicago's Patrick Kane has had six three-point games this year.