The defending Western Conference champion Oilers had lost six of seven to fall to ninth place in the conference. Ales Hemsky and Joffrey Lupul added goals for Edmonton, which opened the scoring with two goals 1:38 apart early in the second period.
Dwayne Roloson finished with 26 saves for the Oilers.
Anson Carter scored his second goal in 14 games for Columbus, which had won two of three, but hasn't won back-to-back games in a month.
After a scoreless first period with both teams' goaltenders stopping quality scoring chances, Hemsky struck 40 seconds into the second.
The Oilers' Toby Petersen scooped up a loose puck in his end after Carter's stuff attempt was blocked. Hemsky took Petersen's pass at centre ice, glided into the zone and fired a wrist shot from the right circle past Pascal Leclaire.
Lupul made it 2-0 with his fourth of the season at 2:18, stepping off the left half-boards and around Columbus' Dan Fritsche before squeezing a snap shot under Leclaire's right arm.
The Blue Jackets missed a prime scoring chance a few minutes later when a crowd of players crashed into Roloson, breaking his stick and forcing him to play without one for nearly two minutes. Columbus was only able get one shot on goal and made a line change before a whistle was finally blown.
Later in the period - and seconds after an Edmonton power play expired - Smyth shed defenceman Ron Hainsey to nudge home a rebound from Steve Staios' point shot to make it 3-0 at 12:40. Smyth has seven points in his last six games.
Columbus responded two minutes later on a power-play rush. Sergei Fedorov slid a cross-ice pass to Rick Nash, who dropped the puck in the slot for Carter. He snapped a shot into the top right corner.
Smyth scored his second goal, and 10th of the season, at 2:07 of the third, redirecting Brad Winchester's pass from the left wing on a 2-on-1 rush. The goal came shortly after the Blue Jackets failed to generate a scoring chance on a 1:37 4-on-3 advantage carried over from the second period.
Notes: Columbus' Ole-Kristian Tollefson and Edmonton's Patrick Thoresen were the first Norwegians to play against one another in the NHL. . . . Edmonton entered with just one win in seven road games. . . . Carter's goal was the 1,000th in Blue Jackets history. . . . Edmonton, which finished 0-for-4 on the power play, was 0-for-18 with the man advantage during their four-game skid.