Mikael Backlund scored with about six minutes remaining to give Calgary the lead and the streaking Flames finally earned their first win in Atlanta, beating the Thrashers 4-2 on Thursday night.
Morrison, Mark Giordano and Curtis Glencross also scored as the Flames earned their sixth straight win, their longest streak in two years. Glencross scored an empty-net goal with six seconds remaining.
The Flames, who played in Atlanta as an expansion franchise from 1972-80, won in Atlanta for the first time in seven games since leaving the South.
"It figured that the law of averages said we were due," Morrison said.
Calgary was winless in six games in Atlanta since the Thrashers joined the league as an expansion team in 1999. The Flames' only point in Atlanta before Thursday night was a 3-3 tie in 2001.
"I guess this was our lucky season," Flames forward Alex Tanguay said.
Bryan Little and Anthony Stewart scored for the struggling Thrashers, who have lost nine of 11 but remained one point ahead of Carolina in the race for the eighth playoff spot in the Eastern Conference. Carolina lost to Toronto 3-0.
Miikka Kiprusoff stopped 22 shots as the Flames moved into a three-way tie with Chicago and Los Angeles for the eighth playoff spot in the Western Conference. The Flames host to Los Angeles on Saturday.
"We have to keep this going," Giordano said. "There are some big conference games coming up. We're finding ways to win close games.
"We've been a good team all year. We feel like we have a strong team. Now is the perfect time to move up in the standings."
Backlund's go-ahead goal came as he shot through a crowd of players in front of goaltender Ondrej Pavelec in the net after the Thrashers were unable to move the puck out of their zone.
"We had the puck three times and threw it right to them," Thrashers coach Craig Ramsay said.
Niclas Bergfors was one of the Atlanta players who at least briefly controlled the puck before a turnover set up Backlund's go-ahead shot.
"I was trying to chip it out the middle," Bergfors said. "I have to look up and make sure someone is there. ... A brutal play by me."
The Thrashers have been outscored 15-5 in their past four games and have scored more than two goals only once in their past nine games.
"Earlier in the year we were winning those close games and finding a way to get that done and not we're finding a way to make that key turnover," Ramsay said. "But the effort was there. It was a much better effort."
Pavelec, who stopped 20 shots, said the Thrashers "had no luck."
"I don't know what to say," Pavelec said. "We played good. We should have won. ... They got two lucky goals."
Calgary's previous six-game winning streak was Oct. 21-Nov. 1, 2008.
Giordano scored immediately after a Flames' power play for a 1-0 lead early in the first period.
Atlanta opened the second period on the attack, tying the game on Little's goal and taking a 2-1 lead midway through the period when Stewart scored on a pass from Evander Kane on a two-on-one rush.
The Flames had a quick answer on Morrison's goal less than a minute later for a 2-2 tie entering the final period.
- The Thrashers placed D Tobias Enstrom on injured reserve with a finger injury before the game. He had missed three straight games. The move is retroactive to Jan. 22.
- Atlanta F Eric Boulton was a healthy scratch for the second straight game.
- Flames LW Niklas Hagman was held out with an undisclosed injury.
- Play was stopped with 2:46 remaining in the second period after Atlanta D Freddy Meyer collapsed at center ice and said after the game he momentarily lost consciousness. Meyer skated off the ice and did not return.