Four minutes into stoppage time, former Japan international Alessandro Santos sent a cross from the left inside the area for Tulio, who headed home to clinch victory seconds before the whistle.
Nagoya now sit on 35 points, only one point behind leaders Shimizu S-Pulse, who were 2-1 winners over defending champions Kashima Antlers in a top-of-the-table battle on Saturday.
Kashima trail them on 34 points, followed by Kawasaki Frontale on 29, Albirex Niigata on 28, with Cerezo Osaka and Gamba Osaka both on 27 points.
Kawasaki drew with Cerezo Osaka 0-0 on Sunday, a day after Niigata defeated Kyoto Sanga 2-0 and Gamba Osaka outclassed Sanfrecce Hiroshima 2-0.
Elsewhere, Vissel Kobe overcame a 10-man disadvantage to upset Urawa Red Diamonds 1-0 thanks to substitute midfielder Masatoshi Mihara's goal in the 52nd minute.