Terry put Anaheim in front 1-0 at 3:17 of the first period. Ryan Getzlaf intercepted a clearing attempt from Andrew Peeke at the Columbus blue line and skated down the right side before sending a pass to Terry for a one-timer.
Bean tied it 1-1 at 4:07 after getting open through the middle of the zone and scoring off a feed from Jack Roslovic.
Terry scored again at 5:43 for a 2-1 lead. He skated through traffic in the slot before scoring on his own rebound in the crease.
It was Terry's 36th goal of the season, the most by an Anaheim player since Corey Perry scored 43 in 2013-14.
"There's a lot of excitement in our room right now," Terry said. "It's been an up-and-down season, but we're excited, and we're excited for next year."
Mayhew pushed it to 3-1 at 7:42 of the first when he redirected a centering pass from Zegras.
"It was definitely a good period for us," Mayhew said. "We came out strong and we controlled most of the play."
Bean made it 3-2 at 1:34 of the second period on a wrist shot from the top of the left circle, and Sean Kuraly tied it 3-3 at 10:52 when he finished a pass from Eric Robinson on a 2-on-0 after Sam Steel turned the puck over in the middle of the zone.
"We found our legs pretty good on a back-to-back, really," Larsen said. "Just big mistakes tonight. That was the thing that really hurt us."
NOTES:Getzlaf, who is retiring after this season, had two assists for his 259th multipoint game with Anaheim, tying Teemu Selanne for the most in its history. … Columbus goalie Elvis Merzlikins had started the previous 11 games. ... Zegras has 57 points (21 goals, 36 assists) in 70 games this season, tying Bobby Ryan for the most by a rookie in Ducks history.