"I think after winning five on the road, it's tough to play any better," Penner said. "It's tough to play any better than that."
Jeff Deslauriers made 30 saves for Oilers.
Penner assisted on the first three goals, the first two from Brule, and added his 18th goal of the season with just under 3 minutes left in the game.
David Backes scored twice and T.J. Oshie added a goal for the Blues. Ty Conklin made his second straight start in place of a healthy Chris Mason and had his shutout streak stopped at 1:33.55 when Brule scored with 11 seconds left in the second period.
Edmonton scored its four third-period goals in just under 9 minutes. Brule got his second goal at the 8:31 mark, and Penner finished the scoring with 2:57 left in the game.
"It's tough to get down three goals," Brule said. "But I think when I got that one late in the second it gave us a big boost. I think we were coming out of it the last seven minutes of the second and all of the third. I don't think they can handle our approach."
Penner's four-point night was his best since he had two goals and three assists against Columbus on Oct. 22. He has also scored a goal in three consecutive games after going two straight without a score.
"I got that feeling, after that second goal and just the way we were playing starting the third period, they were sitting back," Penner said. "Whenever a team does that, if you sit back, it becomes pretty hairy."
Conklin made his second straight start in place of a healthy Chris Mason and had his shutout streak stopped at 1:33.55 after Brule scored the first of his two goals with 11 seconds left in the second. Conklin made 33 saves, including 15 in the third.
He was unavailable for comment after the game.
"It's unacceptable," Blues defenseman Barret Jackman said. "Right after they got that goal at the end of the second period, it seemed like we flipped a switch and we were on our heels and weren't doing the things that got us success in the first two periods. We weren't skating when we got the puck, we were standing still."
Backes was credited with his sixth goal of the season late in the second period after Ladislav Smid redirected the puck into the net. Deslauriers blocked Backes' shot and the puck popped into the air, as it came down Brad Winchester whiffed on his attempt to take a shot and Smid couldn't handle it and pushed it backward.
Oshie added his fifth goal of the season and his first power-play score about seven minutes into the second period to give the Blues a 2-0 lead. Standing alone at the top of the left circle, Oshie took a pass from Paul Kariya and beat Deslauriers with a slap shot to the right of goalie.
Edmonton's Sheldon Souray was given a game misconduct with just over 3 minutes left in the second period. He drew a roughing penalty and officials added a 10-minute misconduct and a game misconduct as he was headed to the penalty box. ... With just over a minute left in the first period, Deslauriers stopped a shot from Oshie but the play was reviewed after the goalie's glove went over the goal line with the puck inside. ... Backes' second goal was reviewed to see if Winchester knocked the puck out of the air with a high stick.