The race to save the city’s off-track betting parlors is headed down the stretch to a nail-biting photo finish.

New York City OTB’s board voted yesterday in an emergency session to keep the parlors open until Tuesday, giving the state Senate a chance to vote on a rescue bill.

The outcome isn’t a sure bet — but the board members decided it was worth delaying a shutdown planned for last night on the chance the Senate will OK a reorganization plan already cleared by the Assembly.

“What changed is the Senate is coming back,” said board member David Cornstein. “I was hopeful that in accommodating them we gave them the time to do the right thing.”

Everyone involved in the rescue effort concedes the Senate lacks the 32 votes needed to pass the Assembly’s bill. Senate Democrats privately estimated that they’ll need about half a dozen GOP votes to save the agency.

Under the plan, 400 OTB workers would lose their jobs and the New York Racing Association, which operates the state’s three thoroughbred racetracks, would take over OTB’s telephone- and Internet-betting systems.