Price stopped Atlanta's first 35 shots before Nik Antropov finally scored 14:14 into the third period to cut Montreal's lead to 2-1. Gionta scored an empty-net goal with 45 seconds remaining.
The Canadiens were outshot 41-23 but stopped the Thrashers' five power plays.
Atlanta coach Craig Ramsay and Montreal coach Jacques Martin agreed Price was the difference.
"I thought their goaltender made some really great saves on us, which increases the frustration," Ramsay said.
Added Martin: "You have to give the win to Carey. He played a strong game."
Price returned after missing one game with the flulike symptoms.
Montreal's Mike Cammalleri said the game "wasn't good on a lot of levels" but looked good in the standings as the Canadiens solidified their hold on sixth in the Eastern Conference.
"That was really good, to win a game when you didn't play very well," Cammalleri said.
The loss was another setback to the Thrashers' playoff hopes. Atlanta ended a five-game skid by beating the Toronto Maple Leafs 3-2 in overtime on Sunday. The Thrashers rallied from a 2-0 deficit against Toronto but couldn't complete the comeback attempt against Montreal.
The Thrashers, who are tied for 10th in the Eastern Conference, have lost 17 of 21.
Pacioretty's unassisted goal in the first period gave Montreal an early lead.
Atlanta's Anthony Stewart was called for crosschecking as the first period ended. Wisniewski's power-play goal 34 seconds into the second pushed Montreal's lead to 2-0.
Stewart complained after the game about the costly penalty which followed his hit on Roman Hamrlik.
"Their guy takes a slap shot at my foot like three seconds after the whistle blows and you have to respond," Stewart said. "I don't think it should have been called. I just gave him a little bump there, but that's the way it goes."
Price, who played in his second All-Star Game this year, was less than six minutes away from his seventh shutout of the season when Antropov scored from outside the left circle. The New York Rangers' Henrik Lundqvist leads the NHL with eight shutouts.
Price withstood four Atlanta power plays in the first two periods. Following Montreal's fourth penalty kill, Atlanta trailed 2-0 despite a 21-6 advantage in shots on goal.
Montreal defenseman Jaroslav Spacek is expected to miss four to six weeks following arthroscopic surgery on his right knee. The team announced the timetable after Spacek visited Dr. James Andrews in Birmingham, Ala. ... Atlanta's Chris Mason stopped 20 shots. ... Thrashers goalie Ondrej Pavelec missed his second straight game with an undisclosed injury. ... The Canadiens were slow on substitutions early and drew two minor penalties for too many men on the ice.
Copyright by STATS LLC and The Associated Press
Arena: Philips Arena Location: Atlanta, Georgia
Referees: Dan O'Halloran, Kyle Rehman Linesmen: Bryan Pancich, Pierre Racicot
Attendance: 11,156 (60.2% full)
Team Stat Comparison
Power Play Goals
Power Play Opportunities
Shots on Goal
Max Pacioretty (12)
James Wisniewski (7)
(Power Play) Assists: Andrei Kostitsyn, David Desharnais
Nik Antropov (11)
Assist: Anthony Stewart
Brian Gionta (23)
(Empty Net) Assists: Scott Gomez, Max Pacioretty