Fast Track to College Act of 2013 - Authorizes the Secretary of Education to award matching six-year grants to local educational agencies (LEAs) that partner with institutions of higher education (IHEs) to establish or support dual enrollment programs, such as early college high schools, that allow secondary school students to earn credit simultaneously toward a secondary school diploma and a postsecondary degree or certificate.

Gives grant priority to applicants: (1) that propose to establish or support a dual enrollment program for a student body at least 40% of which is impoverished; and (2) from states that provide assistance to dual enrollment programs, such as assistance defraying the costs of higher education.

Requires applicants to make assurances that: (1) students will not be required to pay tuition or fees for postsecondary courses, and (2) those courses will be taught by faculty that meet their partner IHE's normal standards.

Authorizes the Secretary to award matching five-year grants to states to: (1) plan and implement statewide strategies to make dual enrollment programs more accessible to students who are underrepresented in postsecondary education; (2) provide technical assistance to dual enrollment programs; and (3) engage in outreach, assessment, and teacher training activities designed to strengthen such programs.

Directs the Secretary to: (1) contract for an independent evaluation of this Act's programs, and (2) provide technical assistance to LEAs and their partners and disseminate information concerning best practices in dual enrollment programs.