We report on interferometric imaging of the CO -->J = 1?0 and -->J = 3?2 line emission from the controversial QSO/galaxy pair HE 0450?2958. The detected CO -->J = 1?0 line emission is found associated with the disturbed companion galaxy, not the luminous QSO, and implies -->Mgal(H2) ~ (1?2) ? 1010 M?, which is 30% of the dynamical mass in its CO-luminous region. Fueled by this large gas reservoir, this galaxy is the site of an intense starburst with -->SFR ~ 370 M? yr ?1, placing it firmly on the upper gas-rich/star-forming end of ultra luminous infrared galaxies (ULIRGs, -->LIR > 1012 L?). This makes HE 0450?2958 the first case of extreme starburst and powerful QSO activity, intimately linked (triggered by a strong interaction) but not coincident. The lack of CO emission toward the QSO itself renews the controversy regarding its host galaxy by making a gas-rich spiral (the typical host of narrow-line Seyfert 1 AGNs) less likely. Finally, given that HE 0450?2958 and similar IR-warm QSOs are considered typical ULIRG ? optically bright QSO transition candidates, our results raise the possibility that some may simply be gas-rich/gas-poor (e.g., spiral/elliptical) galaxy interactions which activate an optically bright unobscured QSO in the gas-poor galaxy, and a starburst in the gas-rich one. We argue that such interactions may have gone largely unnoticed even in the local universe because the combination of tools necessary to disentangle the progenitors (high-resolution and S/N optical and CO imaging) became available only recently.