Perry completed his fourth NHL hat trick by scoring into an empty net in the final minute Sunday night, Selanne had two goals, and the Ducks beat the Blue Jackets 7-4, despite losing goalie Jonas Hiller in the first period.
"We knew this morning when we came to the rink what their record was and what ours was," said Perry, last season's NHL MVP. "Where we are is unacceptable. We have to keep playing. We've had two great games, but we have to keep pushing and doing the right things."
The Ducks, coming off a 4-2 win over the New York Islanders on Friday, have won back-to-back games for the first time since starting the season 4-1. They had scored more than four goals only once in their 39 previous games -- a 6-5 loss to Chicago in Nov. 25.
"We realized that if we lost, we were going to be at rock-bottom. So we didn't want to do that," said Selanne, one of four players left from Anaheim's Stanley Cup-winning team in 2007. "It's unbelievable. It's embarrassing. We want to start climbing up and go from there. And this is something positive to build on.
"We've all been waiting for a moment like this to start rolling and get on a little hot streak, and I still believe we have all the pieces here."
Rick Nash had two goals, and Derick Brassard and Vinny Prospal also scored for the Blue Jackets (11-25-5), who could have moved ahead of Anaheim with a regulation victory. But the Ducks built a 4-1 lead against Steve Mason in the first period after outshooting Columbus 16-8.
Mason, the NHL rookie of the year in 2009, is 5-17-2 with a 3.46 goals-against average this season. He has allowed at least four goals in 12 of his 24 starts -- all losses.
"We weren't prepared from the start," Nash said. "We came out flat and they put the pressure on early. That was the difference. It's been a tough grind on this road trip, and everyone is pretty tired. But we've got to stick with it."
Recently promoted Ducks forward Jean-Francois Jacques received a major penalty for elbowing R.J. Umberger with 5:54 left, 11 seconds after Prospal scored the Blue Jackets' fourth goal. But they couldn't take advantage and lost for the ninth time in 11 games.
"I was looking up at the clock, and the biggest thing I wanted to do was stay positive on the bench -- because sometimes you get negative when something like that happens," Ducks coach Bruce Boudreau said. "They just scored, and then you take a five-minute penalty. Then all of a sudden, the players feed off the negativity. But our penalty killers did a great job."
Cogliano opened the scoring at 2:14. The Ducks made it 2-0 at 13:02 on a play started by defenseman Francois Beauchemin.
Columbus got on the board about 4½ minutes later with a fluke goal by Nash, whose attempted centering pass caromed off Beauchemin's skate and through Hiller's pads. But Selanne and Koivu responded with goals 35 seconds apart in the final 1½ minutes of the first.
"The first period was ugly," Blue Jackets coach Scott Arniel said. "We turned pucks over and we were sloppy as a group. We're a team that has to keep it simple, but it's almost like we complicate it."
The Ducks, 0 for 19 on the power play in the previous six games, ended the drought the second time they had the advantage. Selanne jammed the puck under Mason's left leg after gaining possession behind the net. Koivu made it 4-1 pass 61 seconds before intermission.
But Hiller suddenly headed for the dressing room with an undisclosed lower-body injury and was replaced by backup Iiro Tarkki, who stopped seven of 10 shots in his NHL debut and was credited with the win.
"Hillsy just wasn't feeling right," Boudreau said. "When he made that last save, he looked a little awkward. He said we should just wait until the end of the period, but I wasn't going to take the chance. It's tough to put the poor young goalie into that situation, because sometimes you get overwhelmed."
Tarkki, promoted from Syracuse of the AHL after Dan Ellis strained a groin at practice on Saturday, took a morning flight from Philadelphia after a game at Wilkes-Barre on Saturday.
"Of course I was a little bit nervous when I heard that I was going in. I didn't expect this to happen so fast. It's pretty amazing," Tarkki said. "I didn't have much time to think."
Ellis is expected to be sidelined at least four weeks, putting the Ducks in quite a bind.
"It's a tough break when one of your teammates gets hurt. But on the other hand, it's an opportunity for some other guy," Selanne said.
Mason was replaced at the start of the second period by Curtis Sanford, who beat Los Angeles 1-0 on Saturday for Columbus' first shutout of the season. The Blue Jackets cut the deficit to 4-2 on Brassard's power-play goal at 4:11 of the second.
Staggered penalties 26 seconds apart to Derek MacKenzie for roughing and Samuel Pahlsson for slashing gave Anaheim a two-man advantage, and Perry capitalized with his 17th goal. Selanne added his 651st NHL goal and 14th of the season 27 seconds into the third.
Randy Carlyle, fired as Ducks coach on Nov. 30, visited the press box. ... There had been 11 two-goal games by Ducks players since the team's previous hat trick, by Perry on April 6, 2011, against San Jose. ... Columbus recalled LW Tomas Kubalik from Springfield of the AHL, the second player the team brought up on an emergency basis in a three-day span because of injuries to C Mark Letestu (broken hand) and LW Kristian Huselius (lower body).