Each scored Thursday as the Blues defeated the Columbus Blue Jackets 4-1 at Nationwide Arena.
For Tarasenko, a rookie forward, it was his fifth goal in seven NHL games. Veteran defenseman Jackman connected for the second straight game after scoring just once in a span of 181 games.
"We're not a team that relies on three or six guys," Jackman said. "It's going to be a team effort every night. Some guys put the puck in the net one night and it's going to be picked up by other guys another night."
Three days off did not slow down St. Louis. The Blues have won four in a row and are 6-1-0 after playing six games over the first nine days. They visit Detroit on Friday; a win will give St. Louis its best start since going 7-1-0 to begin the 1997-98 season.
Derrick Brassard scored a power-play goal for Columbus, which was playing for the third time in four nights and has lost six of seven.
"We didn't come out and play hard enough," Columbus forward Brandon Dubinsky said. "That's been a theme the whole year so far. We've got to come out with some fire, with some passion. And we didn't again tonight."
Tarasenko's goal was a highlight-reel effort -- he fought off defenseman James Wisniewski to free himself in the slot and scored before falling to his knees. The 21-year-odl Russian has nine points to tie Tampa Bay Lightning forward Cory Conacher for the rookie lead.
Mason stopped all 13 shots he faced in relief, with Backes scoring his first of the season into an empty net.
"I'm disappointed. It was 3-0, but it wasn't necessarily just the score," Columbus coach Todd Richards said. "It was more how we were playing and how they were playing. Once they scored it seemed like we were right on our heels."
Defenseman Tim Erixon, acquired from the New York Rangers in the offseason trade for Rick Nash, made his Columbus debut. He was a minus-1 with four penalty minutes.
Material from team media and wire services was used in this report