Martin Kaut gave San Jose a 3-2 lead 22 seconds later at 5:14, but Duehr tied it 3-3 at 5:39 with a one-timer off a backdoor pass from Trevor Lewis.
"We fought," Couture said. "Kept it close for a while. I thought we were the better team for the second half the first period. Power play kind of let us down there. It would've been nice to get one at the end to tie that one up.
"Pretty close game overall. We had enough legs to definitely score a fourth one. It's tough. It's tough losing right now."
NOTES: Toffoli has 11 points (five goals, six assists) in his past six games. ... Calgary forward Mikael Backlund was plus-1 in 20:23 of ice time in his 900th NHL game. He is the third player to play in at least 900 games with the Flames, joining Jarome Iginla (1,219) and Mark Giordano (949). ... Karlsson, who leads defensemen in scoring this season, has NHL career highs in goals (22), assists (68) and points (90). ... San Jose signed defenseman Henry Thrun to a two-year, entry-level contract earlier Saturday. He will immediately join the Sharks' roster.