Take the Special Rapid Service bound for Maibara (米原) on the Kyoto (京都) & Biwako (琵琶湖) Line operated by JR West (西日本). It's a silver train.
At Maibara there's a connecting service to Nagoya on the Tokaido Line operated by JR Central (東海). Go to Track 7 or 8.
There's also a limited express called "Urban Liner" between Namba (難波) and Nagoya. 18 kippu is not applicable though. It's not JR but Kintetsu (近鉄).
