This time, they finished off their first-round series.
The Ducks had two goals in the final 2:10 of regulation before Bonino scored on the only shot of overtime for a 5-4 victory over the Dallas Stars that clinched their first-round series.
"I think we said it all along that we learn more from the losses than the wins," said Bonino, who also had one of the tallies late in regulation. "It was always in the back of our minds what happened in Detroit (last year) going into their building with a 3-2 lead and letting it slip away in overtime, so to get it done this way is a lot of fun."
Bonino got the winner on a wrist shot from in front of the net 2:47 into overtime after getting a pass from Andrew Cogliano, and the Ducks advanced in the playoffs for only the second time since winning their lone Stanley Cup title seven years ago.
Anaheim also led its opening-round series 3-2 last year before losing twice to the Red Wings. They had two goals in a 51-second span to tie Game 6 on the road with about 3 1/2 minutes left in regulation before losing in overtime, and then dropped Game 7 at home.
The home team won each of the first five games this series, but Anaheim wanted to take advantage of the first opportunity to close out the upstart Stars.
"With their energy and their speed, we knew it would be deadly in Game 7," said Ben Lovejoy, who scored a second-period goal for the Ducks.
Trevor Daley scored twice on breakaways for the Stars, his first goal coming after he got the puck charging out of the penalty box.
Daley, who also had an assist, is the only current player on the Stars' last playoff team in 2008, when they were eliminated in Game 6 of the conference finals by Detroit in their first season under coach Lindy Ruff.
"Sometimes hockey's cruel," Ruff said. "It was cruel, really cruel, to a group of guys that worked as hard as they possibly could tonight."
Bonino skated around from behind the net and got a puck over Kari Lehtonen's left shoulder to get the Ducks within 4-3 with 2:10 left in regulation.
Anaheim got the overtime-forcing goal with 24 seconds left after a wild scramble in front of the net with an extra skater and Lehtonen without his stick. When the puck trickled free, Devante Smith-Pelly pushed into the open gap for his second goal of the game for a 4-4 tie.
When his team was down two goals, Ducks coach Bruce Boudreau was trying to remain optimistic, even if he didn't expect such a dramatic comeback.
"You're always hopeful. ... But deep down, you don't really think it's going to happen," Boudreau admitted.
"It's still hard to believe. I've got butterflies in my stomach," Bonino said. "Scoring the winning goal in a playoff series is something you play in your driveway when you're a kid."
Corey Perry had the primary assists on both third-period goals for the Ducks, who will wait to see if they play San Jose or Los Angeles in the second round. Teemu Selanne assisted on the first two Anaheim goals.
Jonas Hiller stopped all 12 shots he faced after replacing rookie goalie Frederik Andersen midway through the second period after Daley's second breakaway put Dallas up 4-2. Andersen stopped only eight shots.
"This was a little more special for me. It was a great feeling," said Hiller, who won 29 games during Anaheim's best regular season ever. "When you get the chance, you get so much adrenaline going."
Cody Eakin had a goal and an assist for Dallas, while Lehtonen stopped 25 shots.
Dallas went ahead only 5 minutes into the game when Daley skated around a referee coming out of the penalty box and chased down the puck alone toward the Anaheim net after it was sent down the ice by Shawn Horcoff.
Eakin scored a power-play goal five minutes later, a one-timer on a pass from Tyler Seguin to make it 2-0.
Smith-Pelly had a power-play goal with about 2 minutes left in the first period. But Ryan Garbutt scored a minute later, having been fined but not suspended after spearing Perry and getting a game misconduct midway through the first period of the Ducks' 6-2 win in Game 5 on Friday night.
NOTES: Daley had only two goals in his first 34 career playoff games. ... Selanne (43 years and 207 days) became the second oldest player to record a multi-assist game in the playoffs. Chris Chelios of Detroit had two assists in the 2007 playoffs at 45 years and 102 days. ... Selanne has 66 career playoff points for Anaheim, matching captain Ryan Getzlaf for the most in franchise history. Getzlaf had a goal and two assists in Game 5.