St. Louis is an NHL-best 29-4-4 at home with four games left. The Blues went 29-7-4 at home in 1980-81.
St. Louis, 44-18-7 overall for a league-leading 95 points, has won four in a row and eight of nine.
Elliott, who backed up Jaroslav Halak the last three games, lowered his NHL-best goals-against average to 1.61. The Blues have allowed just one goal in each of the last four games and two or fewer in nine straight.
David Perron, Chris Stewart, T.J. Oshie and Alex Pietrangelo scored for St. Louis, 36-0-0 when scoring three or more goals. Andy McDonald added two assists.
Cam Atkinson scored for Columbus. The Blue Jackets had won four straight.
After Perron opened the scoring in the first period, and Atkinson tied it early in the second, Stewart gave the Blues the lead for good at 9:17 of the second. Stewart powered down the left wing and backhanded a shot from inside the circle over goalie Curtis Sanford while fending off defenseman Brett Lebda.
Oshie made it 3-1 on a power play with 5:22 left in the second, beating Sanford with a one-timer from the right circle. Pietrangelo put it away with another power-play goal with 12:49 left in the third.
NOTES: Oshie's goal was the 2,700th power-play score in team history. ... Columbus hasn't won five straight since Nov. 17-24 2010. . . . The last regulation loss for the Blues in a game in which they scored three times came on March 19, 2011, at San Jose. ... St. Louis is 12-1-1 in its last 14 home games.