We observed the 1991 October outburst of EF Peg. Prominent superhumps with a period of 0.08705(1) d were observed, qualifying EF Peg as a being long-period SU UMa-type dwarf nova. The superhump period showed a monotonous decrease during the superoutburst, which makes a contrast to the virtually zero period change observed during the 1997 superoutburst of the same object. Large-amplitude, and highly coherent quasi-periodic oscillations (super-QPOs) were observed on October 18, when superhumps were still growing in amplitude. Most strikingly, the QPOs showed a rapid decrease of the period from 18 m to 6.8 m within the 3.2-hr observing run. Such a rapid change in the period has not been observed in any class of QPOs in cataclysmic variables. We propose a hypothesis that the rapid decrease of the QPO period reflects the rapid removal of the angular momentum from an orbiting blob in the accretion disk, via the viscosity in a turbulent disk. A brief comparison is given with the QPOs in Xray binaries, some of which are known to show a similar rapid decrease in the periods.