Marcus Tulio Tanaka cancelled out Park Kang-jo's fourth-minute opener with a header six minutes later and Jungo Fujimoto then gave Nagoya the lead when he fired home a Hayuma Tanaka pass in the 61st minute.
J.League top scorer Josh Kennedy sealed the points four minutes from the end, the Australia striker converting substitute Kensuke Nagai's cross for his 15th goal of the season.
Elsewhere, Asian Champions League quarter-finalists Cerezo Osaka warmed up for next week's second leg at Jeonbuk Motors with a 6-0 thrashing of Montedio Yamagata.
Cerezo were without injured Japan midfielder Hiroshi Kiyotake but forward Ryuji Bando opened the scoring for the hosts when he tapped in a Fabio Lopes cross at the far post in the 24th minute.
Kota Fujimoto headed home Hiroyuki Omata's cross to give Cerezo a 2-0 half-time lead before they added two more goals in the early stages of the second period when Noriyuki Sakemoto found the back of the net with a free-kick and Takahiro Ohgihara slotted home Shu Kurata's pass.
Brazilian midfielder Lopes then made it 5-0 when he intercepted a pass and surged up field to score in the 85th minute and, two minutes later, substitute Yohei Ohtake converted a penalty to complete the scoring.
"We are delighted as everyone in our team performed well," said boss Levir Culpi.
"The replacements did well in place of those who couldn't play today due to injury. We can move on to our ACL game with confidence."