  The origin of the solar system abundances of several proton-rich isotopes,
especially $^{92,94}$Mo and $^{96,98}$Ru, has been an enduring mystery in
nuclear astrophysics. An attractive proposal to solve this problem is the $\nu
p$-process, which can operate in neutrino-driven outflows in a core-collapse
supernova after the shock is launched. Years of detailed studies, however, have
cast doubt over the ability of this process to generate sufficiently high
absolute and relative amounts of various $p$-nuclei. The $\nu p$-process is
also thought to be excluded by arguments based on the long-lived radionuclide
$^{92}$Nb. Here, we present explicit calculations, in which both the abundance
ratios and the absolute yields of the $p$-nuclei up to $A\lesssim105$ are
successfully reproduced, even when using the modern (medium enhanced)
triple-$\alpha$ reaction rates. The process is also shown to produce the
necessary amounts of $^{92}$Nb. The models are characterized by subsonic
outflows and by the protoneutron star masses in the {$\gtrsim1.7 M_\odot$
range}. This suggests that the Mo and Ru $p$-nuclides observed in the Solar
System were made in CCSN explosions characterized by an extended accretion
stage.
