The host Mean Green and the Panthers both scored goals within a two-minute period in the second half and had to settle for the draw after two overtime sessions.
The first half was a defensive struggle, but the second half became a shooting frenzy.
North Texas (10-3-2, 5-0-1 Sun Belt) fired 12 shots alone as well as 10 more in the extra sessions. FIU goalkeeper Kaitlyn Savage finished with 16 saves.
It was in the 62nd and 64th minutes that the two teams traded goals.
Scarlett Montoya recorded the first to give the Panthers (6-5-2, 3-1-1) a brief lead, scoring off the cross by Chelsea Leiva.
Karla Pineda tied it for the Mean Green with a dribble penetration shot. It was Pineda’s sixth goal of the season.
North Texas next plays at Arkansas State on Friday.