Mikko Rantanen, Matt Nieto and Nikita Zadorov scored, and Varlamov made 27 saves for the Avalanche (35-24-6), who trail the Los Angeles Kings by one point for the second wild card into the Stanley Cup Playoffs from the Western Conference.
"It's disappointing not to get the two (points)," Avalanche coach Jared Bednar said. "I thought we played well enough to get the two leading late, but it was a good job by our guys coming back in the third period."
Ellis tied it 3-3 with 1:06 remaining in the third period. With the extra skater on the ice, he beat Varlamov from the left circle with a slap shot short side.
"I thought the six guys on the ice did a really good job of setting up and establishing shots and getting into position to where they needed to be," Predators coach Peter Laviolette said. "So, when we shot, we were able to recover. So, we took three, four or five heavy shots there, and the last one went through."