A method and an apparatus for driving a display panel, and a display driver integrated circuit chip are provided. The method includes: determining an order in which display divisions on the display panel are to be driven, when determined not to update respective refresh rates of the display divisions; determining electric signal gear ranges for the display divisions based on the refresh rates of the display divisions, respectively; and driving the display divisions sequentially in the determined order and based on the determined gear ranges. With this method, the power consumption can be reduced while the display effect is improved.