Varlamov made 41 saves in the Colorado Avalanche's 4-3 victory Monday night and beat the Stars for the fourth consecutive time.
Colorado led twice, but both times Seguin scored to tie the game. Seguin has 23 goals this season, but had not scored in 13 games. He also had an assist on Jamie Benn's first-period goal.
Varlamov stopped Seguin twice during a third-period power play with the score tied.
"On Jamie's cross-crease pass, [Seguin] had about 18 inches of open net," Stars coach Lindy Ruff said. "He just pushed the puck back into the goalie's pads."
Varlamov knew he was challenged on that play.
"[Seguin] is a good player. He's got a tough shot. He's pretty skilled. He's always dangerous, especially when we're penalty killing."
The goalie also stopped Seguin's drive from the left faceoff circle as the Avalanche killed the penalty.
Only 19 seconds later, at 4:13 of the third, Tanguay's shot from low in the left circle hit a skate, possibly Dallas defenseman Sergei Gonchar's, and skidded past Stars goalie Kari Lehtonen for the 4-3 lead.
"It wasn't pretty," Tanguay said, "but those things happen. I had [teammate Paul Stastny] at the corner of the net. If it doesn't hit something else, it probably goes in with him."
"The first five minutes," Ruff said. "After that, we dominated. Their goalie stole the show.
"We had five or six point-blank chances in the second to blow the game apart. He was there and he made some great saves."
Alex Goligoski assisted twice for Dallas.
The Avalanche won two of three games on a road trip that ended Monday.
The Stars had won their previous three games by a 14-1 combined margin.
MacKinnon scored after a shot was knocked down in front. The puck went to him just to the left of the goal, and he tapped in a shot before Lehtonen could slide across to that side.
Lehtonen had allowed only one goal in 67 shots during the three previous games.
Colorado scored again at 15:57 of the first period. After blocking a shot by Dallas' Alex Chiasson in their end, the Avalanche attacked. Lehtonen stopped Matt Duchene's shot, but McGinn took the rebound in front and flipped a backhand into the top of the net.
The Stars cut their deficit to 2-1 only 1½ minutes later. Colorado tried to clear from behind the net, but Seguin retrieved the puck on the left wing boards and dropped it to Benn in the faceoff circle. His wrist shot beat Varlamov upstairs for Benn's 20th goal.
Seguin tied the game at 2 with a 4-on-3 power play at 1:02 of the second period. Benn passed from the right circle across to Seguin, who beat Varlamov on the short side.
"It felt good," Seguin said, "like I lost the monkey off my back for sure, getting that goal."
The goal extended Dallas' streak to eight games with a power-play goal (10 total).
The Avalanche regained the lead on Stastny's power-play goal at 17:57. The Stars had successfully killed 16 consecutive penalties before that.
Dallas tied 16 seconds later, when Seguin sent a drive from the right circle under Varlamov's right arm.
"That was my goal," Varlamov said. "I could have moved a little bit, so I was not happy about it. I tried to regroup for myself and get ready for the third period. The third period was huge for us."
He faced a total of 13 shots from the Stars' two leading scorers, eight by Benn and five by Varlamov.
"He's having a great year," Benn said, "and had another good game tonight."
A big difference between third-place Colorado and fifth-place Dallas is that the Avalanche are 13-5-2 within the Central Division, and the Stars are 6-9-5. ... Tanguay has points in six of his past seven games against the Stars. ... MacKinnon has four goals and two assists in his past five games. He and Dallas' Valeri Nichushkin are 1-2 in scoring among rookies. ... Goligoski has seven assists in the past four games, 10 in the past eight. ... Benn has three goals and five assists in the past five games. ... Seguin has four goals and four assists against Colorado this season. ... The season series concluded with the Avalanche 4-1 and Dallas 1-3-1.