Calgary (3-1-0) swept its two-game California road trip and won for the fourth time in its past six games against Los Angeles. Flames goalie Mike Smith stopped 42 of 45 shots and improved his career record to 16-8-1 against Los Angeles.
Los Angeles (2-0-1) got two goals and an assist from Dustin Brown plus a goal and an assist from Anze Kopitar. Jonathan Quick stopped 33 Calgary shots.
Monahan finished off an odd-man rush for his second goal of the season for the win.
The Kings took a 3-2 lead on Brown's two goals in a space of 1:44 early in the third. Brown tipped a shot by Drew Doughty just 14 seconds into the period, then converted a deflection off a Derek Forbort wrist shot for the lead marker. Alex Iafallo earned his first NHL point on Brown's game-tying goal.
Tkachuk tied the game at 3-3 with his second goal of the game at 10:59 of the third period. Tkachuk was left unguarded in the slot on an odd-man break, and his wrist shot trickled past Quick's left pad for the goal. Dougie Hamilton and Frolik earned assists.
Tkachuk gave Calgary a 1-0 lead with a power-play goal at 3:56 of the first period. Tkachuk walked out from the behind the net and converted his own rebound for the score. Mikael Backlund and Mark Giordano recorded assists.
The Flames extended to a 2-0 lead on a goal by Frolik at 7:47 of the first period. Frolik finished off a give-and-go with Johnny Gaudreau, converting a short wrist shot. T.J. Brodie drew the additional assist.
Los Angeles pulled within 2-1 on Kopitar's third goal of the season at 15:44 of the second period. Kopitar took a pass from Jake Muzzin and beat Smith with a snap shot that struck the post to the left of Smith and ricocheted into the net.
NOTES: Flames RW Jaromir Jagr made his debut and finished a minus-1 in 13:38 of ice time. The 46-year-old veteran played in his 1,712th NHL game, and he has 765 career goals and 1,914 points. ... Calgary scratched C Curtis Lazar, C Freddie Hamilton and D Brett Kulak. ... Los Angeles did not dress RW Jonny Brodzinski, C Nic Dowd and D Paul LaDue. ... The Kings continue their five-game homestand against Buffalo on Saturday. ... Calgary returns home to face the Ottawa Senators on Friday.