Optofluidic time-stretch quantitative phase imaging (OTS-QPI) is a powerful tool as it enables high-throughput (>10,000 cell/s) QPI of single live cells. OTS-QPI is based on decoding temporally stretched spectral interferograms that carry the spatial profiles of cells flowing on a microfluidic chip. However, the utility of OTS-QPI is troubled by difficulties in phase retrieval from the high-frequency region of the temporal interferograms, such as phase-unwrapping errors, high instrumentation cost, and large data volume. To overcome these difficulties, we propose and experimentally demonstrate frequency-shifted OTS-QPI by bringing the phase information to the baseband region. Furthermore, to show its boosted utility, we use it to demonstrate image-based classification of leukemia cells with high accuracy over 96% and evaluation of drug-treated leukemia cells via deep learning.