"We made too many mistakes that ended up in the back of our net," Couture said. "We've had some spurts but the mistakes we made we've gone over for years. They're mental mistakes we need to fix."
Couture intercepted a pass from Columbus defender Cody Goloubef right in front of the net and easily beat Bobrovsky to give the Sharks a 4-3 edge with 11:37 remaining.
Pavelski scored his second of the game less than two minutes into the third period, tying it 3-3. He found a seam from the left side of the crease after taking a pass from Joe Thornton.
Burish scored his first of the season, firing a shot past Bobrovsky from the right circle about five minutes into the first period. Pavelski redirected a shot by Couture for a power-play goal late in the first to make it 2-0.
Johansen opened the second-period flurry with a backhander over Niemi's right shoulder.
Less than four minutes later, Letestu scored a short-handed goal off a nice pass from Artem Anismov.
Johansen scored an unassisted goal 83 seconds later after Hartnell knocked the puck loose in the Sharks zone.
NOTES: Columbus gave up its first power-play goal of the season, leaving the Detroit Red Wings as the only team with a spotless penalty-killing unit. ... The Sharks allowed their second short-handed goal of the season. ... Sharks F Patrick Marleau's assist on Pavelski's goal was the 500th of his career. ... Blue Jackets F Jack Skille played in his 200th NHL game. ... The Sharks have outscored opponents 10-1 in the first period but have allowed an NHL-high 23 the rest of the way. ... Thornton has 42 points in 37 games against the Blue Jackets.