Brandon Saad, Mikko Rantanen, Nathan MacKinnon and Valery Nichushkin also scored for Colorado, who recorded their first sweep of the series since defeating Vancouver in the Western Conference quarterfinals in 2001.
The Avalanche beat the Blues 20-7 and trailed only 7:12 in all four games. Grubauer stopped 103 of 110 shots in the four games.
Vladimir Tarasenko scored twice for St. Louis, who was swept away for the first time since losing to the Los Angeles Kings in the second round in 2012.
Landeskog toppled in a shot from Samuel Girard at 2:53 pm of the second period to break a 1-1 draw.
Saad scored from a shot from the high lunge on a pass from Cale Makar a little over three minutes earlier. Grubauer got an assist on the game.
Landeskog finished with two goals and six assists recording a point in every game of the series.
Rantanen flicked his wrist Jordan Binnington with 15:40 left in the third period to push the lead to a 3-1. Rantanen broke in on a 2-1 and took a pass from teammate MacKinnon.
Tarasenko converted on a breakaway on a assist from Ryan O’Reilly for a 1-0 lead at 5:07 of the second period. It was Tarasenko’s first goal since April 26. He added a power play goal with 11:21 left to reduce the deficit to 3-2.
MacKinnon and Nichushkin added goals into an empty net in the last minute.
Binnington made 29 saves.
Colorado has won nine of the last 10 playoff games against St. Louis, including seven in a row.
The Avalanche scored seven goals in an empty net in the series, including two in a 6-3 win in Game 2 and two on Sunday.
Colorado C Nazem Kadri served Game 2 of an eight-game suspension after being hit Justin Faulk in Game 2. This is the sixth suspension of his career. He is appealing the suspension, with the NHL Players Association filing it on Sunday night on behalf of Kadri.
Avalanche: C Alex Newhook left in the first period and did not return after a kick Steven Santini.
Blues: D Justin Faulk, Robert Bortuzzo and Vince Dunn did not play. Dunn has missed the last 15 games with an upper body injury. Faulk and Bortuzzo each suffered head injuries in Game 2.
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