Atlanta scored both goals in the third period, the last by Maxim Afinogenov with 18 seconds left.
"It had never happened for me before. I got lucky. It went in twice," Skoula said.
It was only the third victory in eight games for the defending Stanley Cup champion Penguins (15-8), who have been plagued by injuries after opening the season by winning 12 of 15. The Thrashers (10-7-2) fell to 4-5-1 at home.
Skoula, who had scored only one previous goal this season, gave Pittsburgh a 1-0 lead at 7:38 of the first period. He beat goalie Johan Hedberg with a long shot from mid-ice on the power play.
Skoula made it 2-0 at 7:34 of the second, again on another long blast, easily beating the sprawling Hedberg.
Was he thinking hat trick?
"Not really. I don't think it matters who scores. I'm not in there to score hat tricks," he said.
"I'm happy for him. It's big having a defenseman score two goals," Pittsburgh goalie Mark-Andre Fleury said.
"I felt good. I was pretty relaxed. I tried to set the tempo," said Fleury, who had a shutout until Chris Thorburn scored a short-handed goal 9:40 into the third period.
"We haven't had a shutout [this season]. It would have been huge for us. But it's OK. We won. That's all that matters," he said.
"He [Fleury] was solid. We needed that. He made some big saves," Penguins coach Dan Bylsma said. "For the first 40 minutes, that was probably our best game."
Pittsburgh's Maxime Talbot was awarded a penalty shot with 2:26 left in the second period, but missed the net.
"Fleury made some big saves and we hit a few posts," Hedberg said. "This is a game of margins. Some nights you have them and some you don't."
Pittsburgh outshot Atlanta 34-33.
"We could have been down 4-0 in the second period but Moose [Hedberg] kept us in it. We had a lot of chances but Fleury stood up and made some big saves," Thorburn said.
The Penguins, 8-4 on the road, had lost four straight away from home after a 7-0 start on enemy ice. Sidney Crosby, Pittsburgh's captain and leading scorer with 10 goals and 12 assists, assisted on Skoula's first goal.
Pittsburgh D Brooks Orpik returned after missing four games due to a lower body injury. ... The Penguins were 4-0 against the Thrashers last season and are 27-8-2 overall, including 13-4-2 in Atlanta. ... Afinogenov has six goals and three assists in his last five games.
Copyright by STATS LLC and The Associated Press
Arena: Philips Arena Location: Atlanta, Georgia
Referees: Rob Martell, Dan Marouelli Linesmen: Jonny Murray
Attendance: 17,588 (94.8% full)
Team Stat Comparison
Power Play Goals
Power Play Opportunities
Shots on Goal
Martin Skoula (2)
(Power Play) Assists: Chris Bourque, Sidney Crosby
Martin Skoula (3)
Assists: Matt Cooke, Jordan Staal
Evgeni Malkin (6)
Assist: Mike Rupp
Chris Thorburn (2)
(Shorthanded) Assists: Zach Bogosian, Pavel Kubina