Kiyoshi Okuma's side's looked set to be consigned to a third defeat in their first three games of the new campaign, but they stunned the home side with two goals in stoppage time.
Kosuke Kikuchi and Akihiro Ienaga struck either side of a Tomoki Imai own-goal to put the visitors 2-1 up at half-time.
Reigning champions Sanfrecce Hiroshima's winning start to the season was ended by a 2-0 home defeat against Urawa Reds.
Yokohama F Marinos' impressive start to the season continued as they followed up their Champions League draw with holders Guangzhou Evergrande in midweek by coasting to a 3-0 home win against Tokushima Vortis.
Seitaro Tomisawa put Yasuhiro Higuchi's charges in front 14 minutes in, then second-half strikes from Sho Ito and Jungo Fujimoto ensured the home side maintained their 100 per cent league record after three games, while newly promoted Vortis are bottom of the table without a point.
Takeshi Aoki opened the scoring in the first half at the Best Amenity Stadium, then Yasushi Endo took his tally to four goals in the first three games before Yuta Toyokawa made sure with a third goal to end Tosu's winning start.
Vegalta Sendai and Gamba Osaka played out a goalless draw, while Vissel Kobe secured their first win of the season as Tokyo were consigned to a 2-1 defeat.
