The vast majority of human tumors with p53 mutations undergo loss of the remaining wildtype p53 allele (loss-of-heterozygosity, p53LOH). p53LOH has watershed significance in promoting tumor progression. However, driving forces for p53LOH are poorly understood. Here we identify the repressive WTp53-HSF1 axis as one driver of p53LOH. We find that the WTp53 allele in AOM/DSS chemically-induced colorectal tumors (CRC) of p53R248Q/+ mice retains partial activity and represses heat-shock factor 1 (HSF1), the master regulator of the proteotoxic stress response (HSR) that is ubiquitously activated in cancer. HSR is critical for stabilizing oncogenic proteins including mutp53. WTp53-retaining CRC tumors, tumor-derived organoids and human CRC cells all suppress the tumor-promoting HSF1 program. Mechanistically, retained WTp53 activates CDKN1A/p21, causing cell cycle inhibition and suppression of E2F target MLK3. MLK3 links cell cycle with the MAPK stress pathway to activate the HSR response. In p53R248Q/+ tumors WTp53 activation by constitutive stress represses MLK3, thereby weakening the MAPK-HSF1 response necessary for tumor survival. This creates selection pressure for p53LOH which eliminates the repressive WTp53-MAPK-HSF1 axis and unleashes tumor-promoting HSF1 functions, inducing mutp53 stabilization enabling invasion.