The home victory ensured the Red Wings passed the previous mark set from 1939-58.
"It's pretty good, for sure, getting in 21 straight years," winger Tomas Holmstrom said. "We've had such good teams and we've clinched the play-offs, but we want to win the Stanley Cup."
The Red Wings dominated the Blue Jackets with four goals in the first 10 minutes and extended the lead to 7-0 by the third period before cruising to a win that moved them to fourth in the West on 97 points, one ahead of Nashville.
Holmstrom scored two of Detroit's first three goals, while Henrik Zetterberg and Todd Bertuzzi each had four assists.
The Red Wings also got a goal from defenseman Nicklas Lidstrom for the second straight game as he has proven to be the team's lucky charm.
Lidstrom returned from a 10-game absence because of an ankle and on Saturday and has helped earn consecutive wins following a six-game losing streak.
Gustav Nyquist, Jiri Hudler, Brad Stuart and Pavel Datsyuk all added goals to make a tough night for Columbus goaltender Steve Mason, who was pulled in the second period for the second straight night after allowing six of the scores.
Mark Letestu and Rick Nash each converted late goals for Columbus (24-45-7), who slumped to their seventh loss in nine games and remain burdened with the worst record in the league.
"They took it to us," Nash said. "It showed they are a great team. We weren't ready. (Detroit's playoff streak) is unbelievable.
"It just shows the reputation of their organization and the kind of job they do from the bottom to the top of the organization."
Ty Conklin made 24 stops in the win for Detroit, playing without injured starter Jimmy Howard as well as leading goal scorer Johan Franzen.