Ryane Clowe spoiled Dubnyk's shutout bid, scoring with 3:02 left.
"When it was 5-0, the thought started to creep in," Dubnyk said. "Just a little bit. I didn't get too excited about it. Maybe if I had 20 wins, I might have been a little more desperate to get my first shutout. I was just happy to get another win. Right now I'm just happy to have that winning feeling."
San Jose, coming off losses at Vancouver and Calgary, is 0-5-1 in its last six.
"The frustration level is growing as the days go on," Sharks coach Todd McLellan said. "We didn't really show a lot of emotion in the game until the end of it when it didn't really matter. I'm tired of hearing in our locker room and around the team that adversity is good for us and will pay off in the end.
"It's not going to unless we dig ourselves out of it. There is something missing right now, and we have to figure what it is pretty darn quick."
The Sharks have dropped a point behind Chicago and Phoenix in the race for the top spot in the Western Conference.
"It was quite embarrassing to be honest, to lose that way," goalie Evgeni Nabokov said. "I don't know if this is rock bottom or not, but we are certainly hoping it is. Hopefully we can get back to climbing the hill after this. I think the confidence level is nowhere to be found right now and we have to find it."
On Friday night, Dubnyk beat Detroit in a shootout for his first victory in 14 NHL appearances. He's 2-8-2 overall in his first NHL season.
"This is as close to playoff hockey as we're going to get this year, playing teams that are battling for playoff spots," Oilers forward Sam Gagner said. "We want to treat these situations like playoff games for us, and in the future maybe pull from these experiences."
San Jose had most of the early pressure, including Joe Pavelski's shot that hit the crossbar behind Dubnyk, but Edmonton that struck first, 11:10 into the first period.
Nilsson poked the puck away from Joe Thornton and went in alone, making a nice move on Nabokov to score his 10th goal of the season.
Edmonton made it a two-goal game just over a minute later when the rebound from Ryan Potulny's shot caromed off of a defender to Penner on the doorstep and he was able to slam it home for his 100th NHL goal.
San Jose had a terrific opportunity to cut into the lead with 2 minutes left when Dany Heatley had a clear lane to the net, but couldn't slide the puck under a scrambling Dubnyk.
The Oilers went up 3-0 midway through the second period. Horcoff spotted Tom Gilbert in the slot, and while Nabokov was able to make a glove save on that shot, Pisani was in tight to lift home the rebound.
The Oilers put the game away with 7 minutes left in the third when Ethan Moreau made a great pass through the crease to Horcoff at the other post to make it 4-0.
Edmonton made it a five-goal rout with 5 minutes left when Johnson scored on a shot from the point while the teams were playing four-aside.
Gilbert got his 100th career NHL point with a second period assist. ... Sharks defenseman Marc-Edouard Vlasic returned to the lineup after missing the last 17 games because of a lower-body injury.
Copyright by STATS LLC and The Associated Press
Arena: Rexall Place Location: Edmonton, Alberta
Referees: Dan Marouelli, Marc Joannette Linesmen: Shane Heyer, Mike Cvik
Attendance: 16,839 (100.0% full)
Team Stat Comparison
Power Play Goals
Power Play Opportunities
Shots on Goal
Robert Nilsson (10)
Dustin Penner (27)
Assists: Ryan Potulny, Marc-Antoine Pouliot
Fernando Pisani (4)
Assists: Tom Gilbert, Shawn Horcoff
Shawn Horcoff (12)
Assists: Ethan Moreau, Fernando Pisani
Aaron Johnson (4)
Assists: Dustin Penner, Andrew Cogliano