With the Blue Jackets leading 1-0 early in the first period on Monday night, play was quickly halted when Peverley had a heart problem while on the bench.
Play was halted 6:23 in as Peverley was quickly carried down the tunnel. A public address announcement was made several minutes later that the 31-year-old Peverley was conscious and taken to a hospital.
"We treated (Peverley) for a cardiac event successfully," said Dr. Gil Salazar of UT Southwestern Hospitals. "We provide oxygen for him. We started an IV. We did chest compressions on him and defibrillated him, provided some electricity to bring a rhythm back to his heart, and that was successful with one attempt, which is very reassuring.
"As soon as we treated him, he regained consciousness. He was able to tell me where he was."
A hush fell over the crowd during the lengthy delay between the time play was stopped and when the game was called off.
There was no immediate announcement of when the game would be made up.
"Dallas player Rich Peverley is doing well and is in stable condition," the NHL said in a statement. "As a result of the emotional state of the players on both teams caused by the medical emergency, the game is being postponed. We apologize for any inconvenience and we thank the fans."
Peverley's wife, Nathalie, accompanied him in the ambulance to UT Southwestern St. Paul University Hospital.
The Stars conveyed the message to the Blue Jackets that they weren't up for finishing the game on Monday.
"They're shaken and they want to reschedule. We understand that," John Davidson, the Blue Jackets president of hockey operations, told Fox Sports Ohio. "They were shaken to the core."
Peverley missed the preseason and the season opener because of a procedure to correct an irregular heartbeat, a condition diagnosed during a training camp physical. He made his Stars debut on Oct. 5 against Washington.
"We monitor him closely for a different type of arrhythmia he has," Dr. Salazar said. "He does have a pre-existing condition, and the condition -- a normal quivering of the heart that does not allow him to send blood to places where he needs to, in his brain and heart."
Peverley sat out last week's game at Columbus because of an irregular heartbeat. He had felt strange after last Monday's game and couldn't fly.
Peverley then played in Dallas' next two games before Monday.
"There wasn't any concern," Stars coach Lindy Ruff said regarding Peverley's return to the lineup. "Our doctors have done a fabulous job monitoring the situation."
Both teams skated off the ice after Peverley's collapse. The Stars didn't go directly through the tunnel next to their bench, but through a door at the south end of the rink.
"I was scared," Ruff said.
As Ruff turned to seek medical help from the stands, players from both teams tried to attract the officials' attention by banging their sticks on the boards and the ice.
"If it wasn't for our doctors and all the members (of the training staff) reacting so quickly, I could be standing here with a different story," Ruff said. "They were there ASAP. It's an absolute marvel after what he went through."
The scene inside the arena was tense before the news of Peverley's condition improved.
"When he dropped, it was red alert," Ruff said. "Don't worry about the game. It was about getting the doctors.
"As soon as he came off the ice, I started screaming into the crowd for a doctor. The players don't want to play, and I don't want to coach the team right now."
In 62 games this season before Monday, Peverley had seven goals and 23 assists.
"The first thing (Peverley) asked me was how much time was left in the first period," Ruff said.
Ruff wouldn't speculate on whether the Stars might seek to have Tuesday's game at St. Louis postponed.
"He's going to be OK," Ruff said. "The care he's getting and the care going forward is the most important thing."