Gagner followed up on his eight-point game in Edmonton's 8-4 win over Chicago. He also scored in the shootout.
"It's a big win for us," Gagner said. "Especially the way we did it, coming back at the end. I knew I wasn't going to get another eight-point night. But even after the points kept coming our line was still creating.
"I'm just feeling way better about how I am playing. I want the puck. I want to be the guy."
The Oilers blew a 3-1 lead in the third period but sent it to overtime when Jordan Eberle scored with 39 seconds left.
Eberle ended up with a pair of goals for the Oilers, who have won three in a row and are 4-0-1 in their last five games.
"We were good for two periods and then sat around and watched them play in the third," Oilers coach Tom Renney said. "That's very dangerous against one of the best teams in the league. But we collected ourselves and played more intelligent and showed some character."
Detroit almost got on the board first before the game was 2 minutes old. Darren Helm had a short-handed breakaway, but Oilers starter Devan Dubnyk was able to come up with a clutch save.
The Oilers made good on the power play a minute later as Gagner knocked the rebound of Ryan Whitney's shot past Red Wings goalie Ty Conklin.
"Sam has been a lot of fun to watch," Nugent-Hopkins said. "I'm really happy for him. It was a big character win for us."
Gagner got his second point of the night just before the 6-minute mark of the first. He put the puck on net, and it slipped beneath Conklin and went to Eberle, who scored his 21st of the seasons.
Edmonton retained the lead after killing off a two-man disadvantage. Corey Potter was given a double-minor for coming to the aid of teammate Ales Hemsky after he was crushed along the boards by Niklas Kronwall. An additional penalty to Edmonton's Ladislav Smid left the team down two players for a full 2 minutes.
Gagner had a direct result on two more goals to close out the first period, one by each team.
With 37 seconds to play, Gagner coughed up the puck to Filppula in his own zone on the power play. Filppula fanned on his shot but it hit Whitney's stick and trickled into the Oiler net, just out of the reach of a diving Dubnyk, for the short-handed goal.
Gagner redeemed himself with less than a second left in the period on the same power play as he tipped in a Ryan Smyth shot for his second of the game. It was the 11th consecutive Edmonton goal that Gagner got a point on, all within a three-period span going back to the second period of the win over Chicago.
Recent call-up Joey MacDonald started the second period in the Detroit net.
Detroit made it a one-goal game 2 minutes into the third as Henrik Zetterberg fed it to Bertuzzi from behind the net and he whacked at the puck under Dubnyk.
The Red Wings tied the game 3-all only 3 minutes later as Helm got the puck through to Miller in front of the net and had an easy redirect for his 10th of the year.
Detroit took a 4-3 lead with just under 4 minutes to go as Bertuzzi showed some skill, passing it to himself through defenseman Andy Sutton's legs before beating Dubnyk up high.
With Dubnyk on the bench, the Oilers sent it to extra time as Eberle found the puck in a scramble in front and put it past MacDonald.
"It's disappointing to lose the extra point when we had the lead with under a minute to play," Red Wings captain Nicklas Lidstrom said. "We came back from a 3-1 deficit to tie the game up and then took the lead. So it's tough to take when you lose after battling back like that."
It was the third of four meetings between the two teams this season. Detroit won the first two games by 3-0 and 3-2 scores. The Oilers came into the game with seven straight losses to the Red Wings. ... Detroit G Jimmy Howard was out with a broken finger. ... Dubnyk made his career-high fifth consecutive start in goal for Edmonton. ... After an injury-filled season, the Oilers are almost back to full strength as the league's rookie points leader, Nugent-Hopkins, returned to the lineup after missing the last 13 games with a shoulder injury. D Tom Gilbert, the only Oiler still on the IR, is expected to play early next week. ... Bertuzzi was able to play after being listed as questionable going in with a charley horse.
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EDMONTON, CANADA - FEBRUARY 4: Sam Gagner #89 of the Edmonton Oilers warms up before a game against the Detroit...