Diffuse interstellar bands (DIBs) are weak and broad interstellar absorption features in astronomical spectra that originate from unknown molecules. To measure DIBs in spectra of late-type stars more accurately and more efficiently, we developed a random forest model to isolate the DIB features from the stellar components. We applied this method to 780 thousand spectra collected by the Gaia Radial Velocity Spectrometer (RVS) that were published in the third data release (DR3). After subtracting the stellar components, we modeled the DIB at 8621{AA} ({lambda}8621) with a Gaussian function and the DIB around 8648{AA} ({lambda}8648) with a Lorentzian function. After quality control, we selected 7619 reliable measurements for DIB {lambda}8621. The equivalent width (EW) of DIB {lambda}8621 presented a moderate linear correlation with dust reddening, which was consistent with our previous measurements in Gaia DR3 and the newly focused product release. The rest-frame wavelength of DIB {lambda}8621 was updated as {lambda}0=8623.141+/-0.030{AA} in vacuum, corresponding to 8620.766{AA} in air, which was determined by 77 DIB measurements toward the Galactic anticenter. The mean uncertainty of the fit central wave-length of these 77 measurements is 0.256{AA}. With the peak-finding method and a coarse analysis, DIB {lambda}8621 was found to correlate better with the neutral hydrogen than with the molecular hydrogen (represented by ^12^CO J=(1-0) emission). We also obtained 179 reliable measurements of DIB {lambda}8648 in the RVS spectra of individual stars for the first time, further confirming this very broad DIB feature. Its EW and central wavelength presented a linear relation with those of DIB {lambda}8621. A rough estimation of {lambda}0 for DIB {lambda}8648 was 8646.31{AA} in vacuum, corresponding to 8643.93{AA} in air, assuming that the carriers of {lambda}8621 and {lambda}8648 are comoving. Finally, we confirmed the impact of stellar residuals on the DIB measurements in Gaia DR3, which led to a distortion of the DIB profile and a shift of the center (<~0.5{AA}), but the EW was consistent with our new measurements. With our measurements and analyses, we propose that the approach based on machine learning can be widely applied to measure DIBs in numerous spectra from spectroscopic surveys.