Kawai (2-1) allowed the Eagles just a single and a pair of infield hits during a 111-pitch outing before handing the baton to closer Hitoski Iwase, who pitched a perfect ninth to collect his 17th save.
Hirata hit a two-out, solo drive in the second inning and Masahiro Araki's suicide squeeze followed Yohei Oshima's one-out triple for the second run in the third. Catcher Motonobu Tanishige doubled down the right-field line to plate the decisive run in the seventh.
Dragons manager Morimichi Takagi said after the day's 1-0 win over the Hanshin Tigers at Nagoya Dome, ''We'll give Yoshimi some time to recover from the injury. We'll remove him from the active roster.''
Yamasaki hit his third home run of the spring with a solo shot off fellow veteran Fumiya Nishiguchi in the second inning of a 3-2 loss to the Seibu Lions at Seibu Dome on Tuesday.
The 43-year-old two-time home run leader will now likely bat cleanup and play first base in Chunichi's season-opening game against the Hiroshima Carp on March 30, having outperformed Tony Blanco in exhibition play.
''I would like to make my presence felt in the startingrotation,'' said Kawakami, who returns to Chunichi for the first time in four years, ahead of the 2011 Central League champion's spring training camp in Okinawa getting under way Wednesday.