Plasma is a complex system involving diverse collisional processes and interactions, such as electron-impact excitation, ionization, recombination, etc. One of the most important methods for studying the properties and dynamics of plasma is to analyze the radiations from plasma. Here, we demonstrate the high-order harmonic (HH) spectroscopy for probing the complex electron-atom collision (EAC) dynamics in a laser-induced gas plasma. These measurements were carried out by using an elliptically polarized pump and a time-delayed linearly polarized probe. The HH spectra from argon and krypton plasmas were recorded by scanning the time delay up to hundreds of picoseconds. We found that the delay-dependent HH yield contains three distinct regions, i.e., the first enhancement, the subsequent suppression, and the final restoration regions. A qualitative analysis shows that these features are clear signatures of the EAC processes and interactions involved in the delay-dependent HH spectroscopy.