Heatley opened the scoring with his 13th goal 1:18 in, and set up goals by Spezza and Alfredsson later in the period.
"We knew they played last night and obviously tried to get the jump on them early," Alfredsson said. "It was nice to get some goals early, to help settle us down a little bit. We probably won the game in the first period."
Brendan Bell added his first goal in six games with Ottawa in the second, and Shean Donovan scored the Senators' fifth goal late in the third. Alex Auld stopped 22 shots.
Ottawa improved to 3-1-2 in its last six games following a skid that saw it lose four straight in regulation.
Eric Boulton scored his first goal in 47 games for Atlanta, which lost 5-4 in Montreal on Tuesday night.
"It doesn't really feel that hot," Boulton said. "It's nice to be on the board, but it didn't mean anything."
The Thrashers have lost five in a row (0-4-1), and eight of nine.
Boulton scored his first goal since Feb. 5 just 1:35 after Heatley's goal to draw Atlanta even. Spezza got his eighth goal on a power play at 6:12 to restore Ottawa's lead.
"We're expected to generate offense when we play together and we did a good job of tonight of finding each other," Spezza said.
Alfredsson, who assisted on Heatley's goal, made it 3-1 when he scored his seventh goal at 15:31. The Ottawa captain recovered the puck with his backhand after Heatley flicked it ahead and moved it to his forehand before slipping it under Ondrej Pavelec's left pad.
"We got a little bit more time and space than we usually do, probably because they played [Tuesday] night, and we exploited that a little bit," Alfredsson said.
Bell scored Ottawa's second power-play goal 18:54 into the second for his first NHL goal since Jan. 20.
Donovan increased the Senators' lead to four with his fourth goal 16:29 into the third.
Many spectators in the Scotiabank Place crowd of 17,215 got a shock when they witnessed a man falling about 25 feet from the upper deck during the second intermission.
According to witnesses, the 21-year-old man sailed headfirst past and over a few stunned onlookers in the rows ahead of his seat before clearing the low railing at the bottom of the third level and falling onto a row of seats in the level immediately below.
Following the game, Senators president and CEO Roy Mlakar confirmed the accident, which he said was the first of its kind in the arena's 13-year history.
Mlakar said the man, who was conscious while receiving on-site treatment for lacerations, was taken to a hospital as a precautionary measure. Mlakar also said two of the people the man landed on were treated at the arena and that a third person, a 33-year-old woman, had sustained a non-critical neck injury, and also was taken to hospital for precautionary reasons.
Thrashers D Mathieu Schneider missed his second straight game because of an upper-body injury. ... The Senators' top line acquired its nickname from a pizza chain promotion that originally kicked in when Ottawa scored five goals in a game. It was subsequently raised to six goals.