Homeless Veterans Prevention Act of 2013

Homeless Veterans Prevention Act of 2013 - Requires public or private nonprofit entities that receive grants under the Department of Veterans Affairs (VA) comprehensive service programs for homeless veterans to agree to meet the physical, privacy, safety, and security needs of such veterans.

Increases the per diem payment for transitional housing assistance for homeless veterans who are placed in housing that will become permanent upon the termination of such assistance to a maximum of 150% of the per diem rate authorized for veterans receiving domiciliary care in state homes.

Allows services for which a homeless veteran receives a grant under the comprehensive service programs to include furnishing care for a dependent.

Directs the Secretary of Veterans Affairs (Secretary) to: (1) assess and measure the capacity of programs for which entities receive grants or per diem payments to assist homeless veterans, and (2) use such information to ensure that such programs effectively serve the needs of such veterans. Repeals a required annual VA report on activities under such programs.

Repeals the September 30, 2013, sunset on the authority of the Secretary and the Secretary of Labor to carry out a program of referral and counseling for veterans who are at risk of homelessness and are transitioning from certain institutions, including penal institutions.

Authorizes the Secretary to enter into partnerships with public or private entities to provide legal services to homeless veterans and veterans at risk of homelessness.

Revises VA authority to provide dental care to veterans receiving certain other assistance through the VA to include those veterans receiving assistance under the United States Housing Act of 1937.

Extends permanently the VA comprehensive service programs for homeless veterans. Extends temporarily various VA authorities and programs affecting homeless veterans.