Brandon Saad, Robert Thomas and Jordan Kyrou also scored in St. Louis’ first game since a 4-2 loss at Winnipeg on Dec. 19. Jordan Binnington made 26 saves in his second start since being activated off the COVID-19 list.
"We had a lot of time to rest," Tarasenko said. "I know a lot of guys spent it with families. It gives you more positive emotions."
Leon Draisaitl and Evan Bouchard scored for Edmonton in its first game since a 5-3 win at Seattle on Dec. 18. Mike Smith stopped 29 shots.
"I thought we did some things right," Oilers center Ryan Nugent-Hopkins said. "Overall, we just gave them too many good opportunities and Smitty had to make some big saves."
Tarasenko gave the Blues a 3-2 lead on his 13th goal of the season when he skated to the edge of the crease and pushed the puck past Smith with 4:14 remaining in the second period. Tarasenko has scored in four straight games, compiling five goals and four assists during that span.
Saad added his 12th of the season 16 seconds into the third on a power play to make it 4-2.
Thomas, centering Kyrou and Tarasenko, scored his third goal after a give-and-go with Tarasenko 4:03 into the first period.
"They played really well," Blues coach Craig Berube said about that line. "Not just the goals, but just the overall play. I thought they possessed pucks and did good things with it. I thought they worked hard without the puck and were committed defensively. That's a big part of it."
Kyrou scored his 10th nearly three minutes later, becoming the fifth Blues player to reach double figures this season.
"I think our team’s super deep," Kyrou said. "It's great that we have a lot of guys who can score and a lot of guys keep making plays. Also, everyone defensively is doing really well."
Draisaitl cut St. Louis' lead to 2-1 when he got his 24th of the season just 32 seconds later.
Bouchard scored his sixth on a shot from outside the faceoff circle that snuck past Binnington to tie it 2-all with 8:11 remaining in the second.
"We made a couple mistakes early, got behind early, and chased the game," Oilers coach Dave Tippett said. "We were around a little bit, but turned over a lot of pucks and wound up chasing. When you’ve been off 11 days, that’s not an ideal situation."
Berube earned his 200th victory as an NHL coach, making him the seventh in league history to win 200 games and play in at least 1,000. Berube played in 1,054 games over 17 seasons.
"It means a lot," Berube said. "It’s a credit to a lot of people for sure, throughout your career and life who helped you along the way."
WELCOME TO THE NHL
Oilers D Dmitri Samorukov made his NHL debut. The 22-year-old was a third-round pick by the Oilers in the 2017 draft.
Blues LW Pavel Buchnevich was scratched with a non-COVID-19 illness. St. Louis dressed 11 forwards and seven defensemen.
Oilers: At the New Jersey Devils on Friday.
Blues: At the Minnesota Wild on Saturday to compete in the Winter Classic at Target Field.