Dan Fritsche led the way with a goal and two assists while Alexander Svitov, Gilbert Brule and Anson Carter also scored for Columbus (7-16-2).
The Oilers (13-10-2) have lost three in a row following a four-game winning streak. Edmonton also faces the possibility of an extended period without Smyth, who leads the team with 16 goals in 25 games. The talented forward left the game in the first period and did not return.
It's the latest bad break for the Oilers, who lost third-leading scorer Ales Hemsky to a shoulder injury two games earlier in a loss to Anaheim. He's expected to miss one-to-two weeks.
The Blue Jackets opened the scoring almost nine minutes in when Svitov's soft wrist shot from the high slot beat Oilers starter Dwayne Roloson five-hole to give Columbus a 1-0 lead after a listless first period.
The Oilers continued to struggle early in the second period, registering only one shot on a four-minute power-play opportunity.
Roloson didn't help his own cause, taking a slashing call on Rick Nash that came back to haunt him on the ensuing power play. Ron Hainsey's shot from the point hit the crossbar and landed flat behind Roloson. Gilbert Brule vaulted into the crease and poked it in.
The bleeding continued for Edmonton just a minute and half later when a Columbus pass bounced off the skate of Edmonton defenceman Daniel Tjarnqvist right to the waiting stick of Carter. The former Oiler fired his fourth goal of the season past a diving Roloson.
Columbus outshot the Oilers 14-5 in the second.
For the second game in a row Jussi Markkanen replaced Roloson in goal, coming on in relief to start the third. He only faced three shots before being yanked with a minute left, and Fritsche closed the scoring with an empty-netter.
Notes: Smyth has 12 goals and 12 assists in 21 career games against Columbus, including a two-goal performance earlier this year in a 4-1 win over the Blue Jackets. ... Columbus won for just the second time in 11 trips to Edmonton. The Oilers lead the overall series 14-3-5. ... The Oilers head to Vancouver on Monday before returning home on Wednesday for a Stanley Cup final rematch with the Carolina Hurricanes.