Only one other player in Flames lore has had a longer run of goals to begin a season. But at this rate, Gary Roberts' five-game stretch in the 1989-90 season looks to be in peril.
No. 28 is running that hot.
Andrew Mangiapane had the Flames' other tally, and Dan Vladar - playing in his first regular-season tilt with the club - posted 22 saves in the victory.
Lindholm scored a pair in regulation and then the winner, 2:46 into overtime, off a lovely dish on a 2-on-1 with Johnny Gaudreau.
With the win, the Flames improve to a perfect 2-0-0 on the road trip, and 2-1-1 overall this season.
The Caps got the first great chance of the game less than 100 seconds in, as Evgeny Kuznetsov intercepted the puck in the neutral zone, split the D and scooted in alone, but his quick, blocker-side bid caught iron.
The homeside kept the pressure on and forced the Flames into a sloppy line change. A too-many-men penalty ensued, but the PK turned in a huge effort and kept the high-powered Caps offence at bay.
From there, the Flames went on the attack, recording four of the next five shots on goal, and earning a powerplay of their own when former Flame Garnet Hathaway was tagged for roughing.
The visitors made him pay, with the second unit doing the damage.
Noah Hanifin sailed a shot through from the point, handcuffing a partially screened Vitek Vanecek. With the rebound sitting loose in the blue paint, Mangiapane swooped in and chopped home his third of the year, putting the Flames up 1-0 at 9:27.