New York City’s jobless rate fell to its lowest level since April 2009 last month as hiring in professional services, education and health care helped lead to a gain of 51,200 jobs in the past year.

The city’s unemployment rate dropped to 9.1 percent last month on a seasonally adjusted basis, from 9.2 percent in October, the state Department of Labor said today. The rate was 8.9 percent in April 2009 and reached 10.5 percent in November of that year.

Statewide, the seasonally adjusted jobless rate rose to 8.3 percent, after the Labor Department revised its October level to 8.2 percent from an earlier estimate of 8.3 percent.

City private-sector employment increased by 1.6 percent over the 12 months ending in November, to about 3.2 million, primarily in professional services, education, health care, tourism and transportation. Financial-services employment increased by 5,900 during that period, mostly in credit-granting and real estate, the department reported.

“By historical standards, these numbers are quite strong,” James Brown, a Labor Department economist, said in a telephone interview. “Gains over the year are quite broad with losses only in manufacturing and publishing and information. It’s the result of national economic growth in industries where the city is strongest.”