The Rangers piled up all their runs over the first four innings for a 9-4 lead but the A's made things interesting with home runs by Yoenis Cespedes, Brandon Moss and Josh Reddick to cut the deficit to two runs in the eighth.
The win went to starter Matt Harrison (18-10), who gave up four runs and seven hits in six innings.
Oakland starter Travis Blackley (5-4) allowed five runs on five hits and didn't come out for the second inning.
Kinsler hit Blackley's second pitch for a home run and Napoli capped the rally with a two-run shot for his 21st home run of the season.
Reddick, who had two of Oakland's five home runs, hit a homer in the second but Josh Hamilton had an RBI double for the Rangers for a 5-1 lead. Both teams scored single runs in the third and twice in the fourth. Derek Norris hit a two-run homer for Oakland while Aldus single in a run and scored the other in the Rangers' fourth.