Kelsey Cunningham kicked a 21-yard field goal with just 4.4 seconds remaining in the fourth quarter to send the Rockets to a 17-14 victory.
It is the Rockets first state title since 2009, and comes a year after a 28-27 loss to Aztec.
Jalen Chavez scored two touchdowns in the game for Los Lunas. The second – a four-yard reception from quarterback Chris Wisnewski — gave the Tigers a 14-7 lead early in the fourth quarter.
But Goddard stormed back and tied the game with five minutes to play before taking the win.
A controversial pass interference call against Los Lunas on the final drive of the game set the Rockets up inside the Los Lunas 20-yard line with 35 seconds to play.
In the 5A state championship game, Las Cruces claimed its seventh state title in school history with a 35-28 win against Sandia.