Kyohei Noborizato's 63rd-minute winner gave the visitors - who were reduced to 10 men with five minutes remaining when Paulinho was sent off - all three points at the Best Amenity Stadium.
The result means Kawasaki now sit just one point adrift of Sagan in the table.
League leaders Urawa Reds took full advantage of Sagan's defeat as they moved four points clear at the summit with a routine 2-0 victory at bottom-placed Tokushima Vortis thanks to goals from Tomaki Makino and Shinzo Koraki.
Kashima Antlers remain in the hunt for an AFC Champions League spot despite their poor run of form continuing with a 2-2 draw against lowly Omiya Ardija.
Toninho Cerezo's side had won just one of their last five top-flight games going into the fixture, and Omiya twice equalised after going behind at the Kashima Soccer Stadium.
Reigning champions Sanfrecce Hiroshima hammered Kashiwa Reysol 5-2 to move up to fifth, while Vissel Kobe were held to a 1-1 draw at Yokohama F Marinos.
Vegalta Sendai and Nagoya Grampus were involved in a six-goal thriller at the Yurtec Stadium.
Nagoya came from behind three times to earn a point, with Leandro Domingues' injury-time equaliser snatching a draw.
Meanwhile, Shimizu S-Pulse - who are now without a win in seven outings - slipped closer to relegation danger by succumbing to a 4-0 reverse at mid-table Gamba Osaka.
Elsewhere on Wednesday, Tokyo moved up to ninth with a 1-0 away win at Albirex Niigata, and Cerezo Osaka played out a 0-0 stalemate with Ventforet Kofu.