Danis Zaripov had three assists, while Alexei Morozov added a pair of helpers for Russia, which has defeated Denmark in all six World Championship contests going back to April of 2003.
Evgeni Nabokov turned aside 15-of-18 shots, before suffering an undisclosed injury in the third period and was replaced by Konstantin Barulin, who stopped all four shots. Russia will next face the Czech Republic on Sunday.
Nichlas Hardt scored a pair of goals and Mikkel Bodker had the other for Denmark, which was without captain Morten Green due to a shoulder injury.
Frederik Andersen made 36 saves for the Danes, who will meet Germany on Saturday.
Artyukhin backhanded home a rebound 5:21 into the third to give the Russians a 4-2 lead. The Danes cut the deficit to one just over two minutes later on a tally by Hardt, but were unable to get the equalizer in the remaining time on the clock.
In Group F play in Kosice, Jonas Holos had a goal and an assist, as Norway got by Switzerland 3-2.
Per-Age Skroder and Kristian Forsberg also lit the lamp for the victors, who will meet Canada on Saturday. Lars Haugen was stellar between the pipes, turning aside 39 shots.
It was Norway's third straight win over the Swiss in World Championship competition, dating back to 1993.
Raphael Diaz and Thibaut Monnet each had a goal for Switzerland, which will take on Sweden on Sunday.