Brandon Saad, Mikko Rantanen, Nathan MacKinnon and Valeri Nichushkin also scored for Colorado, which recorded its first series sweep since beating Vancouver in the 2001 Western Conference quarterfinal round.
The Avalanche outscored the Blues 20-7 and trailed for only 7:12 over the four games. Grubauer stopped 103 of 110 shots over the four games.
“I thought we got a little better as the series went along,” Colorado coach Jared Bednar said. “It was a full 60-minute effort. The first three games we had some lapses in our game, some things that I didn’t like. Tonight, I liked a lot.”
Vladimir Tarasenko scored twice for St. Louis, which was swept for the first time since losing to the Los Angeles Kings in the second round in 2012.
Landeskog tipped in a shot from Samuel Girard at 14:53 of the second period to break a 1-1 tie.
“To come in here in a tough building to play and take two in a row against a desperate team, it’s not easy to do,” Landeskog said. “I’m happy that we got it done without giving them any sort of momentum.”
Saad scored on a shot from the high slot off a pass from Cale Makar just over three minutes earlier. Grubauer got an assist on the play.
Landeskog finished with two goals and six assists in recording a point in every game of the series.
“You break down each game and I think the score hasn’t really been indicative of the way the series has been,” Landeskog said. “It’s been really tight, it’s hard checking and it hasn’t been easy. Coming in here in a tough building to play in and take two in a row against a desperate team, it’s not easy to do.”
Landeskog said the Avalanche used a pre-series boast from St. Louis captain Ryan O’Reilly as motivation. O’Reilly claimed the Blues were going to win the series.
“Yeah, it did,” Landeskog said. “It was a hard fought series.”
Rantanen whipped a wrist shot past Jordan Binnington with 15:40 left in the third period to push the lead to a 3-1. Rantanen broke in on a 2-on-1 and took a pass from linemate MacKinnon.
Tarasenko converted on a breakaway off a pass from 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 trim the deficit to 3-2.
MacKinnon and Nichushkin added empty-net goals in the final minute.
Binnington made 29 saves.
Tarasenko was not pleased with the effort of his team.
“This is embarrassing always losing in the playoffs,” Tarasenko said. “The answer is there are no excuses. We don’t fight enough.”
St. Louis coach Craig Berube said that injuries, especially to the Blues’ back line, were a factor in the series, but he would not offer that as an excuse.
“They’re the better team, for sure,” Berube said. “We’ve got to get better, we’ve got to improve.”
Colorado has won nine of the last 10 playoff games against St. Louis, including seven in a row.
The Avalanche scored six empty-net goals in the series, including two in a 6-3 win in Game 2 and two on Sunday.
Colorado C Nazem Kadri served the second game of an eight-game suspension after hit to Justin Faulk in Game 2. It is the sixth suspension of his career. He is appealing the suspension, with the NHL Players’ Association filing it Sunday night on Kadri’s behalf.
Avalanche: C Alex Newhook left in the first period and did not return after a hit from Steven Santini.
Blues: D Justin Faulk, Robert Bortuzzo and Vince Dunn did not play. Dunn missed the last 15 games with an upper-body injury. Faulk and Bortuzzo each suffered head injuries in Game 2.