"This is a tough one," Lightning coach Jon Cooper said. "Tied game with under five minutes to go. I thought we were getting points from this one. We let them slip out of our hands."
Thompson has eight goals, and four of them have come in a pair of two-goal games. He got his first one Sunday when he beat Varlamov on the short side 6:40 into the second period to tie it at 2.
Later in the period, he sent a wrister at Varlamov that settled in the crease, and then he skated through to knock it in at 17:37.
The Lightning missed an opportunity to move into second place in the Atlantic Division and third in the Eastern Conference after Colorado's late-game eruption.
"I think we're going through a little bit of a rough patch," Thompson said. "A couple breakdowns there at the end and they end up in the back of the net, unfortunately."
Colorado stayed within three points of St. Louis in the Central Division with the win. The Blues beat Phoenix on Sunday.
The game was scoreless for most of the first period despite plenty of chances. Lightning center Vladislav Namestnikov had two of them and Colorado center Matt Duchene was stopped on a breakaway.
Tampa Bay finally cashed in when Pyatt scored at 16:49 of the first. Barrie tied it 30 seconds later with a shot between Bishop's legs, and O'Reilly gave Colorado a 2-1 lead with his 23rd of the season 1:42 later.
NOTES: Duchene and Nathan MacKinnon finished with two assists. ... Tampa Bay C Valtteri Filppula missed his fourth straight game with a non-displaced fracture in his right ankle. ... MacKinnon extended his points streak to 11 games. It's the longest streak by a rookie since Stastny had one of 20 games during the 2006-07 season.