Equal Access to Quality Education Act of 2013 - Directs the Secretary of Education to award competitive matching grants to partnerships between high-need local educational agencies (LEAs) and institutions of higher education (IHEs) to establish or support: (1) teacher preparation programs, and (2) teacher induction and retention programs.

Requires the teacher preparation programs to: (1) require participants to complete at least one year of residency followed by at least three years of teaching at the LEA's high-need schools, and (2) award participants a teaching credential or degree that meets state requirements for a teaching license or certification upon completion of the program.

Requires the teacher induction and retention programs to use high-quality mentoring, teacher collaboration, and research-based instructional practices to: (1) support and advance the retention of beginning teachers and principals, and (2) promote effective teaching and leadership skills.

Allows the grants to be used for certain other activities designed to improve the quality of education in high-need areas.

Gives grant priority to partnerships that: (1) use a valid and reliable teacher performance assessment and have a plan to recruit teachers from among minority and local candidates and the disabled; or (2) use that assessment and include an IHE that is eligible to participate in the TEACH Grant program, a Tribal College or University, an Asian American and Native American Pacific Islander-serving institution, a Hispanic-serving institution, or a historically Black college and university.