Flames netminder Miikka Kiprusoff recorded 34 saves as Calgary (20-10-4) joined Colorado at the top of the Northwest standings.
"I thought our team played hard here tonight," Flames coach Brent Sutter told reporters.
"It was positive in the sense that we wanted to get back to playing more like we can. We'll certainly take the win. It was a big two points for us."
The Kings (22-12-3), tied with the San Jose Sharks atop the Pacific division and Western Conference standings, have not beaten the Flames in Calgary since December 2005, a string of eight successive losses.
Calgary took the lead when Phaneuf converted a power-play slap shot with a second remaining in the first period. Nigel Dawes made it 2-0 early in the third before Corey Elkins pulled one back for the Kings at 11:06.
Phaneuf, a former Norris Trophy finalist for the league's top defenseman, had six of his seven goals in the season's first nine games before going ice cold.
"Sometimes they go in, sometimes they don't," said Phaneuf, who had failed to find the net since November 5 in St. Louis.
"I was hitting posts, getting pucks on net. It was a big one for me to get, but I've been there before."
Jonathan Quick made 22 saves for Los Angeles.
(Writing by Jahmal Corner in Los Angeles; Editing by Peter Rutherford)