Bachman, a fourth-round 2006 draft pick by the Stars, made only his third career appearance and initial career start. He responded by allowing only a Brad Richardson short-handed goal in the second period.
Trevor Daley got the eventual game-winner with 3:16 left in the middle frame. He picked up loose puck in the slot and fired a wrist shot into the net, which Kings goalie Jonathan Bernier partially blocked.
Jamie Benn also scored for Dallas, which won for only the second time in seven road games.
Bernier finished with 26 saves for the Kings, who dropped their fourth straight.