Varlamov made 38 saves and the Avalanche beat Calgary Flames 4-1 on Friday.
Colorado matched San Jose with 88 points, one behind Dallas and Phoenix for the last two playoff spots in the Western Conference. The Avalanche have home games left against Columbus and Nashville. Phoenix, Dallas and San Jose each have four games left.
"We've got five days off now until our next game. We're just going to have to wait and see what happens," Colorado coach Joe Sacco said. "Certainly, our young group has played hard all year and I think we deserve to be in this position that we're in down the stretch."
Jarome Iginla had a power-play goal for Calgary with 38 seconds left.
The Flames, who have three games remaining, fell three points behind Colorado and could be eliminated Saturday night when they play in Vancouver.
Calgary is 1-4-3 in its last eight games.
"In the last eight games, that's probably been the worst defensive games I've seen this team play all year and that's why our offense has struggled," Flames coach Brent Sutter said. "You can't score seven goals in seven games when you're having 20-some goals scored against you. It doesn't work."
Gabriel Landeskog had two assists for Colorado to taking the lead in the NHL rookie scoring race with 51 points. The 19-year-old Swede also lead rookies in plus-minus at plus-23 after being a plus-3 against Calgary.
"I'm not one of those guys that sits at home and watches Sports Center all day. I'll leave that up to the other guys and just do my own thing, get my rest, and get my mind off hockey a little bit," Landeskog said. "But it will definitely be a little nerve racking for sure.
"We have a bright future," said Landeskog. "We have a great group of guys in here, we're really upbeat and positive for the next couple years, regardless of what happens this year."
The best stops for Varlamov, making his seventh consecutive start, came in the first period, just before Colorado scored its first two goals.
Seconds before Olver opened the scoring, the 23-year-old goalie stopped Curtis Glencross' one-timer from the side of the net. And before Colorado's second goal, Varlamov denied Mike Cammalleri from the slot.
- The Flames will likely miss the playoffs for the third straight season and 10th time in 15 years.
- Iginla's last-minute goal snapped Calgary's shutout stretch on home ice at 139:50.
- Colorado didn't have a power play, the seventh time that's happened this season.