Context. One of the key noise sources that currently limits high-contrast imaging observations for exoplanet detection is quasi-static speckles. Quasi-static speckles originate from slowly evolving non-common path aberrations (NCPA). These NCPA are related to the different optics encountered in the wavefront sensing path and the science path, and they also exhibit a chromatic component due to the difference in the wavelength between the science camera and the main wavefront sensor. These speckles degrade the contrast in the high-contrast region (or dark hole) generated by the coronagraph and make the calibration in post-processing more challenging. Aims. The purpose of this work is to present a proof-of-concept on-sky demonstration of spatial Linear Dark Field Control (LDFC). The ultimate goal of LDFC is to stabilize the point spread function (PSF) by addressing NCPA using the science image as additional wavefront sensor. Methods. We combined spatial LDFC with the Asymmetric Pupil vector-Apodizing Phase Plate (APvAPP) on the Subaru Coronagraphic Extreme Adaptive Optics system at the Subaru Telescope. To allow for rapid prototyping and easy interfacing with the instrument, LDFC was implemented in Python. This limited the speed of the correction loop to approximately 20 Hz. With the AP-vAPP, we derive a high-contrast reference image to be utilized by LDFC. LDFC is then deployed on-sky to stabilize the science image and maintain the high-contrast achieved in the reference image. Results. In this paper, we report the results of the first successful proof-of-principle LDFC on-sky tests. We present results from two types of cases: (1) correction of instrumental errors and atmospheric residuals plus artificially induced static aberrations introduced on the deformable mirror and (2) correction of only atmospheric residuals and instrumental aberrations. When introducing artificial static wavefront aberrations on the DM, we find that LDFC can improve the raw contrast by a factor of 3-7 over the dark hole. In these tests, the residual wavefront error decreased by ∼50 nm RMS, from ∼90 nm to ∼ 40 nm RMS. In the case with only residual atmospheric wavefront errors and instrumental aberrations, we show that LDFC is able to suppress evolving aberrations that have timescales of < 0.1-0.4 Hz. We find that the power at 10 −2 Hz is reduced by a factor of ∼20, 7, and 4 for spatial frequency bins at 2.5, 5.5, and 8.5 λ/D, respectively. Conclusions. We have identified multiplied challenges that have to be overcome before LDFC can become an integral part of science observations. The results presented in this work show that LDFC is a promising technique for enabling the high-contrast imaging goals of the upcoming generation of extremely large telescopes.