A drunken Jersey City cop whose speeding car mowed down an aspiring lawyer in the Financial District last year was sentenced yesterday to serve at least 3½ years of prison.

Relatives of Martin Abreu, 26, broke into sobs as he was led off.

Abreu was off-duty in February 2009 when he plowed into Marilyn Huang Feng and her boyfriend, a hedge-fund analyst, on West Street.

The two, both 26, had been walking home after a tango lesson.

The boyfriend, Dennis Loffredo, suffered a shattered leg and the loss of “the love of his life,” said the prosecutor, William Beesch.

Abreu’s maximum sentence is 10.5 years.