The wins represent major victories for Democrats in New York. All three outcomes were widely expected based on pre-election opinion polls.
Incumbent Gov. David A. Paterson, a Democrat, did not run for re-election.
Cuomo, 52, is the son of Mario M. Cuomo, who was New York's governor from 1983-1994 and is now a New York City lawyer.
Paladino, 64, is a Buffalo real estate developer and political neophyte whose strident rhetoric failed to gain support from voters, exit polls indicated.
"The people of the state of New York want a government that they can trust, a government that they can be proud of once again, the government that they deserve -- and they are going to get it," Cuomo, who will be New York's 56th governor, said in a victory speech in New York City.
In key congressional races, Democratic U.S. Rep. John Hall, representing the Hudson Valley region just above the New York City suburbs, lost to wealthy Republican ophthalmologist Nan Hayworth, a Tea Party movement favorite, and Democratic Rep. Scott Murphy lost his seat to retired Army Col. Chris Gibson.
Incumbent Rep. Maurice Hinchey, an influential Democrat, defeated Republican challenger George Phillips in the sprawling 21st Congressional District, which extends west from the Hudson River along New York's southern border through Binghamton and north to Ithaca.
In the extreme northern frontier of the state bordering Lake Ontario and the Adirondack Mountains, Democratic Rep. Bill Owens defeated investment banker Matt Doheny, and west of Albany, the state capital, Democratic Rep. Michael Arcuri lost to businessman Richard Hanna, unofficial results indicated.
In state races, Democratic state Sen. Eric T. Schneiderman defeated Republican Daniel M. Donovan Jr. in the race to succeed Andrew Cuomo as attorney general. He ran a campaign pledging to keep the heat on the Wall Street financial industry and to restore trust in state government.
Incumbent Democratic state Comptroller Thomas P. DiNapoli narrowly defeated Republican Harry J. Wilson, a Wall Street trader turned first-time candidate, by about 3 percentage points.