Gavrikov connected off a tic-tac-tie feed from Cole Sillinger to Yegor Chinakhov for his fifth game-winning goal and second OT score this season.
''It was 3-on-1, and I just was ready,'' Gavrikov said. ''I had only one option. If I get the puck, I have to shoot.''
Boone Jenner scored twice, Eric Robinson had a goal and an assist, Sean Kuraly added a goal and Gavrikov also had an assist for Columbus, which picked up points in its third straight game. Elvis Merzlikins stopped 15 shots before leaving in the second period with a leg injury, and Joonas Korpisalo stopped 18 in relief.
''We are finding ways to get some points here,'' Jenner said. ''It starts with our energy and our forecheck, kind of getting our legs under us and scoring.''
Kevin Hayes and Noah Cates each had a goal and an assist, Nick Seeler scored and Travis Konecny added a power-play goal for the Flyers, who rallied twice from two goals down to force overtime and earn a point. Carter Hart stopped 28 shots in his third straight loss.
''We started forechecking, had more energy, and found a way to lose,'' Flyers coach John Tortorella said. ''We score four tonight and we still lose.''
Kuraly gave Columbus the lead at 12:36, burying the rebound of a Gavrikov's shot for his first goal after missing two games with a concussion.
Jenner made it 2-0 at 5:36 of the second with his second power-play goal of the season, burying the bounce of Johnny Gaudreau's shot from the left circle.
Philadelphia pulled within one at 8:54 with Hayes one-timer right in front of Merzlikins before Cates tied it off the rush at 12:16.
That was the last shot faced by Merzlikins, who had to be helped off the ice.
Jenner next beat Hart on a breakaway at 3:32 of the third to put Columbus back on top, and Robinson made it 4-2 just 13 seconds later.
''They're playing hard,'' Blue Jackets coach Brad Larsen said. ''We lost ourselves a bit in the second period there, especially the last 10-12 minutes, but we got ourselves together. The guys are are giving it. They're playing hard.''
The Flyers, however, were not done and Seeler made it 4-3 at 4:58 before Konecny pulled them back even at 9:14.
FEELING THE POWER
Columbus has scored a power-play goal in four of its last five games after starting the season 0-25 with a man advantage.
HOME SWEET HOME
Gaudreau's assist on Jenner's goal continued his points tear at Nationwide Arena, as he has recorded six goals and five assists in 10 games.
Konecny stretched his point streak to seven games, and continues to lead the Flyers in goals and assists with 18 and seven, respectively. Hayes has contributed six points (3-3) in the last six games.
The Blue Jackets welcomed back Kuraly off injured reserve after he missed two games with an upper-body injury. The Flyers recalled Max Willman from the Phantoms.
One game after scoring his first career goal, Marcus Bjork added his first career assist on Robinson's goal. Bjork scored in his NHL debut Sunday against the New York Islanders, becoming just the seventh CBJ player in team history to do so.
HE SAID IT
''It sucks.'' Flyers coach John Tortorella when asked in the first period what he thought of his team's effort.
Flyers: At Boston on Thursday night.
Blue Jackets: Host Montreal on Thursday night.
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