Tkachuk put the Flames up 4-1 at 4:24 when he shot five-hole off the rush on a setup by Gaudreau.
Lundstrom scored shorthanded to cut it to 4-2 at 4:26 of the third period. The goal, his third in the past two games, tied a Ducks record for most shorthanded goals in a season at four.
"Even after the first it's 2-0, I think we had some good opportunities that we obviously didn't score on," Shattenkirk said. "At the end of the day, it's still 2-0. That's a tough lead to come back on, especially against a team like that. That lapse we had in the second is really what shot us in the foot."
Gaudreau scored into an empty net to make it 5-2 at 16:48, and Andrew Mangiapane scored his team-leading 25th goal of the season at 17:51 for the 6-2 final.
NOTES: It's the Flames' longest winning streak since their 10-game run during the 2016-17 season. … Lindholm (seven goals, six assists) and Gaudreau (four goals, eight assists) each extended his point streak to eight games. Gaudreau got his 367th career assist and passed Mark Giordano for fifth in Flames history. … Calgary has scored four or more goals in seven straight. ... Dube has goals in back-to-back games after ending a 13-game drought in a 6-2 win against the Columbus Blue Jackets on Tuesday. ... Tkachuk has scored nine points (three goals, six assists) in a five-game point streak. ... Ducks forward Rickard Rakell had his three-game goal streak end. … Anaheim went 0-for-5 on the power play.