James Wisniewski added two assists for the Blue Jackets. Steve Mason turned-aside 18 shots, including three key saves with the Ducks on the power play and pressing for the tying goal in the second period.
The Ducks have lost five of six and are 1-2-1 on their 13-day, seven-game road trip.
Circling with the puck around the right circle, Nash waited for R.J. Umberger to screen Ellis, then he pulled up and snapped a shot from the dot for his fourth of the season at 2:23.
Anaheim got on the board six minutes later with an end-to-end, 2-on-1 rush. Selanne cut through center ice, stretched it wide before sliding a puck past Kris Russell to Ryan, who fired a shot top shelf for his fourth.
The game turned chippy with three fights in five minutes. Ducks captain Ryan Getzlaf squared off with Cody Bass in one bout.
Columbus also struck early in the second period on Johansen's second goal of the season at 1:57. Countering after a Ducks turnover at the attacking blue line, Johansen, on a superb individual effort, stepped around Lubomir Visnovsky at center ice, collected his balance and burst in on Ellis, scoring near post on his backhand.
With Anaheim on its second man-advantage of the period, Mason made three lead-preserving saves. He kicked aside two quick shots from Corey Perry and then smothered a point-blank shot on the next sequence by Koivu streaking alone down the slot.
Tyutin extended the lead to two for the Blue Jackets with a point shot through traffic for his second at 12:52.
In the third period, the Blue Jackets weathered a steady Anaheim attack and pushed back midway through with a solid penalty kill.
NOTES: It was the fourth straight game Columbus has faced a backup goalie. ... Ellis dropped to 5-1-1 all-time against the Blue Jackets. ... Columbus plays four of their next five at home. ... The Blue Jackets are 2-3-1 at home and 0-6-0 on the road. ... The Ducks, who finished 0 for 3 on the power play, are 1-5-1 in one-goal games.