The mass of one of the three major waiting points in the astrophysical rp process 72Kr was measured for the first time with the Penning trap mass spectrometer ISOLTRAP. The measurement yielded a relative mass uncertainty of deltam/m=1.2x10(-7) (deltam=8 keV). (73,74)Kr, also needed for astrophysical calculations, were measured with more than 1 order of magnitude improved accuracy. We use the ISOLTRAP masses of 72-74Kr to reanalyze the role of 72Kr (T(1/2)=17.2 s) in the rp process during x-ray bursts and conclude that 72Kr is a strong waiting point delaying the burst duration with at least 80% of its beta-decay half-life.