Plasma dynamics are governed not only by temperature and density but also by macroscopic flows. However, velocity fields (vflow) inside laser-produced plasmas (LPPs) have rarely been measured, owing to their small size (< 1 mm) and short lifetime (< 100 ns). Here, we report, for the first time, two-dimensional vflow measurements of Sn-LPP for extreme-ultraviolet (EUV) light sources for semiconductor lithography using the collective Thomson scattering technique, which is conventionally used to measure electron temperature and density. We discovered plasma inflows exceeding 104 m/s toward a plasma central axis, which plays an important role in improving the total EUV light emission, i.e., plasma inflows maintain the EUV source at a temperature suitable for EUV light emission for a relatively long time and at a high density. These results indicate that controlling the plasma flow can improve EUV light output and that there is sufficient potential to increase the EUV output further.