The inmates got out of the sprawling, privately owned and operated Logan Hall facility in Newark after cell doors clicked open when the power went out during the storm, investigators said.
Inmates burst into hallways, tearing up furniture, defacing inspirational signs and threatening female inmates, The New York Times reported Sunday.
Fifteen escaped and all but one have been caught, officials said.
The facility houses parolees and people awaiting trial on criminal charges, the Times said.
After the chaos broke out, 50 law enforcement officers were called in, most from their homes, to help quell the unruly prisoners, the Times said.
The facility's operator, Community Education Centers, has come under fire lately from critics who say there has been lax oversight of New Jersey's halfway house system.
William J. Palatucci, a top executive at Community Education Centers and a friend and political adviser to Gov. Chris Christie, announced he will step down in the wake of the Logan Hall incident, the Times said.
A state corrections department spokesman said there were no injuries to law enforcement personnel or inmates and the matter had been blown out of proportion.
An investigation of the state's halfway house program by the newspaper in June revealed that 5,200 inmates had escaped since 2005, some by simply walking out an unguarded and unlocked front door of a facility. Others left a halfway house on work-release program and never returned.
Of the prisoners who escaped during the storm, several had been convicted of weapons possession, assault and burglary, officials said.