The knockout stages of the 2013 Copa Libertadores de América were played from April 24 to July 24, 2013. A total of 16 teams competed in the knockout stages.[1]
The winners and runners-up of each of the eight groups in the second stage qualified for the knockout stages.
| Group | width=190 | Winners | width=190 | Runners-up |
|---|---|---|---|---|
| 1 | Nacional |  Boca Juniors | ||
| 2 |  Palmeiras | Tigre | ||
| 3 | Atlético Mineiro | São Paulo | ||
| 4 | Vélez Sarsfield |  Emelec | ||
| 5 | Corinthians |  Tijuana | ||
| 6 |  Santa Fe |  Real Garcilaso | ||
| 7 | Olimpia | Newell's Old Boys | ||
| 8 | Fluminense | Grêmio |
The qualified teams were seeded in the knockout stages according to their results in the second stage, with the group winners seeded 1–8, and the group runners-up seeded 9–16.
In the knockout stages, the 16 teams played a single-elimination tournament, with the following rules:[1]
The bracket of the knockout stages was determined by the seeding as follows:[1]
The first legs were played on April 24–25 and April 30–May 2, and the second legs were played on May 8–9 and 14–16, 2013.[2]
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----Atlético Mineiro won 6–2 on aggregate.
----Tied 2–2 on aggregate, Santa Fe won on away goals.
----Olimpia won 3–2 on aggregate.
----Boca Juniors won 2–1 on aggregate.
----Tied 2–2 on aggregate, Newell's Old Boys won on away goals.
----Fluminense won 3–2 on aggregate.
----Tied 1–1 on aggregate, Real Garcilaso won on penalties.
----Tijuana won 2–1 on aggregate.
The first legs were played on May 22–23, and the second legs were played on May 28–30, 2013.[3]
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----Tied 3–3 on aggregate, Atlético Mineiro won on away goals.
----Santa Fe won 5–1 on aggregate.
----Olimpia won 2–1 on aggregate.
----Tied 0–0 on aggregate, Newell's Old Boys won on penalties.
The first legs were played on July 2–3, and the second legs were played on July 9–10, 2013.[4]
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----Tied 2–2 on aggregate, Atlético Mineiro won on penalties.
----Olimpia won 2–1 on aggregate.
See main article: 2013 Copa Libertadores Finals.
The finals were played on a home-and-away two-legged basis, with the higher-seeded team hosting the second leg. The teams tied on aggregate, the away goals rule was not used, and 30 minutes of extra time were played. A penalty shoot-out was used to determine the winner.[1]
The first leg was played on July 17, and the second leg was played on July 24, 2013.[5]
----Tied 2–2 on aggregate, Atlético Mineiro won on penalties.