Discharge lamp lighting device and lighting fixture

One output power characteristic curve for supplying constant power is provided with respect to a raging voltage range of a discharge lamp, and in addition, a plurality of output power characteristic curves W, W and W are provided with respect to a lamp voltage before the rating voltage range. There is provided minimum lamp voltage detecting means for detecting a minimum lamp voltage after a high intensity discharge lamp shifts to an arc discharge in an event where lamp power is supplied to a high intensity discharge lamp based on any initially set output power characteristic curve after the high intensity discharge lamp is started. As the minimum lamp voltage detected by the minimum lamp voltage detecting means is larger in a predetermined minimum lamp voltage range, any larger output power characteristic curve is reset from the plurality of output power characteristic curves W, W and W, and subsequent power control is performed.