NEW YORK — Democrats have won a majority in New York’s Senate to give the party control of the full Legislature and governor’s office for the first time since 1935.

Democrats, who outnumber Republicans by a nearly 2:1 ratio statewide, ended more than 40 years of GOP rule in the Senate thanks in part to the enthusiasm fueled by Barack Obama’s historic presidential campaign.

Democrats won at least 32 seats in the 62-seat chamber. They trailed 31-29 with two vacancies going into Tuesday.

The vote comes after record spending on both sides and gives Democratic Gov. David Paterson, just seven months on the job, a new ally along with the Assembly.

Lee Miringoff of the Marist College poll says the win will put pressure on Democrats to break Albany’s notorious gridlock.