The crash happened at the intersection of Tompkins and Myrtle avenues in Bedford-Stuyvesant just before 10:30 p.m.
Authorities say the incident began with Housing Authority police officers observing a man identified as 27-year-old Wilbert Rodriguez, of Pennsylvania, damaging a parked car with a baseball bat.
When the officer intervened, the suspect reportedly jumped into his vehicle, with another man inside, and tried to flee the scene.
While making his getaway, police say Rodriguez brushed his vehicle against the three officers, then slammed into the van, flipping it over on to its side.
The 66-year-old van driver is in critical but stable condition with a broken jaw and other injuries at Woodhull Hospital. The officers are were treated and released from Wyckoff Hospital.
The suspect and passenger, 23-year-old Abrenim Rodriguez-Quezada, of Queens, suffered various minor injuries.
Rodriguez is charged with assault on a police officer, assault, criminal mischief, reckless endangerment, aggravated unlicensed operator of a vehicle, traffic device violation and driving at an imprudent speed.
Rodriguez-Quezada is charged with criminal mischief.