We demonstrate high-order harmonic generation in Ni-doped CsPbBr3 perovskite nanocrystals ablated by nanosecond pulses using chirp-free 35 fs, and chirped 135 fs pulses in the case of single-color pump (800 nm) and a two-color pump (800 nm and 400 nm). We analyzed the spectral shift, cut-off, and intensity distribution of harmonics in the case of chirped drving pulses compared to chirp-free pulses. It is shown that the presence of Ni dopants and CsPbBr3 plasma components improves the harmonics emission. Also, we measured the third-order nonlinear optical (NLO) properties of these nanocrystals using 800 nm, 60 fs, 1 kHz pulses. The variations of measured NLO parameters of CsPbBr3 perovskite nanocrystals containing different concentrations of nickel correlate with variations of generated high-order harmonics from laser induced plasmas of studied nanocrystals in terms of harmonics intensity, cut-off, and spectral shift (in case of chirped driving pulses). The spectral shift of the harmonics generated from the Ni-doped CsPbBr3 perovskite nanocrystals can be used to form tunable extreme ultraviolet sources.