We present MAMBO 1.2 mm observations of five BzK-pre-selected vigorous starburst galaxies at z~2. Two of these were detected at more than 99.5% confidence levels, with 1.2 mm fluxes around 1.5 mJy. These millimeter fluxes imply vigorous activity with star-formation rates (SFRs) approx. 500-1500 Msun/yr, confirmed also by detections at 24 microns with the MIPS camera on board of the Spitzer satellite. The two detected galaxies are the ones in the sample with the highest SFRs estimated from the rest-frame UV, and their far-IR- and UV-derived SFRs agree reasonably well. This is different from local ULIRGs and high-z submm/mm selected galaxies for which the UV is reported to underestimate SFRs by factors of 10-100, but similar to the average BzK-ULIRG galaxy at z~2. The two galaxies detected at 1.2 mm are brighter in K than the typical NIR-counterparts of MAMBO and SCUBA sources, implying also a significantly different K-band to submm/mm flux ratio. This suggests a scenario in which z~2 galaxies, after their rapid (sub)mm brightest phase opaque to optical/UV light, evolve into a longer lasting phase of K-band bright and massive objects. Targeting the most UV active BzKs could yield substantial detection rates at submm/mm wavelengths.