After Tamada opened the scoring in the 27th minute, Nagoya failed to take several more scoring chances, but international goalkeeper Seigo Narazaki and defender Marcus Tulio Tanaka fended off Yamagata attacks.
"We haven't lost to lower-ranked teams this season. That's why we are top now. We must steady ourselves not to be beaten by pressure," said Tamada, who scored his seventh goal of the season.
Tulio said: "It's the best way of winning, because we've been tired after the summer and players are getting injured."
Nagoya have now 47 points from 15 wins, two draws and five defeats, ahead of Cerezo Osaka and defending champions Kashima Antlers on 40 points each. They are followed by Shimizu S-Pulse on 39 points, then Gamba Osaka and Yokohama Marinos on 37 points each.
In today's other game, former Asian club champions Urawa Red Diamonds beat FC Tokyo 1-0 thanks to a penalty from by Brazilian midfielder Ponte in the 66th minute.
Urawa's German coach Volker Finke was delighted with the away win despite missing several regular starting players. "I'm really glad that we took three points like this. It's really good that younger players helped the team win today," said Volker.
Yesterday, Cerezo Osaka were held to a 1-1 draw by Sanfrecce Hiroshima, while Kashima defeated Vegalta Sendai 1-0.