Ryan Ellis and Yakov Trenin scored in regulation for Nashville, which has won four of five.
Roope Hintz and Jamie Oleksiak scored for Dallas, which had its two-game winning streak snapped.
It was the fourth time in seven games between the teams this season that they have gone to overtime.
Hintz scored the gameâs first goal at 4:56 of the opening period. From the left boards, John Klingberg sent a pass to Hintz in the high slot, where beat Nashville’s Juuse Saros with a one-timer.
Saros finished with 24 saves and denied all three of Dallas’ attempts in the shootout.