diff --git a/doc/source/whatsnew/v1.2.0.rst b/doc/source/whatsnew/v1.2.0.rst
index 8b28a4439e1da..bd4ee9b46db67 100644
--- a/doc/source/whatsnew/v1.2.0.rst
+++ b/doc/source/whatsnew/v1.2.0.rst
@@ -289,6 +289,7 @@ MultiIndex
 I/O
 ^^^
 
+- :func:`read_sas` no longer leaks resources on failure (:issue:`35566`)
 - Bug in :meth:`to_csv` caused a ``ValueError`` when it was called with a filename in combination with ``mode`` containing a ``b`` (:issue:`35058`)
 - In :meth:`read_csv` `float_precision='round_trip'` now handles `decimal` and `thousands` parameters (:issue:`35365`)
 - :meth:`to_pickle` and :meth:`read_pickle` were closing user-provided file objects (:issue:`35679`)
diff --git a/pandas/io/sas/sas7bdat.py b/pandas/io/sas/sas7bdat.py
index 76dac39d1889f..f2ee642d8fd42 100644
--- a/pandas/io/sas/sas7bdat.py
+++ b/pandas/io/sas/sas7bdat.py
@@ -142,8 +142,12 @@ def __init__(
             self._path_or_buf = open(self._path_or_buf, "rb")
             self.handle = self._path_or_buf
 
-        self._get_properties()
-        self._parse_metadata()
+        try:
+            self._get_properties()
+            self._parse_metadata()
+        except Exception:
+            self.close()
+            raise
 
     def column_data_lengths(self):
         """Return a numpy int64 array of the column data lengths"""
diff --git a/pandas/io/sas/sas_xport.py b/pandas/io/sas/sas_xport.py
index 1a4ba544f5d59..9727ec930119b 100644
--- a/pandas/io/sas/sas_xport.py
+++ b/pandas/io/sas/sas_xport.py
@@ -264,7 +264,11 @@ def __init__(
             # should already be opened in binary mode in Python 3.
             self.filepath_or_buffer = filepath_or_buffer
 
-        self._read_header()
+        try:
+            self._read_header()
+        except Exception:
+            self.close()
+            raise
 
     def close(self):
         self.filepath_or_buffer.close()
diff --git a/pandas/io/sas/sasreader.py b/pandas/io/sas/sasreader.py
index ae9457a8e3147..31d1a6ad471ea 100644
--- a/pandas/io/sas/sasreader.py
+++ b/pandas/io/sas/sasreader.py
@@ -136,8 +136,8 @@ def read_sas(
     if iterator or chunksize:
         return reader
 
-    data = reader.read()
-
-    if ioargs.should_close:
-        reader.close()
-    return data
+    try:
+        return reader.read()
+    finally:
+        if ioargs.should_close:
+            reader.close()
diff --git a/pandas/tests/io/sas/data/corrupt.sas7bdat b/pandas/tests/io/sas/data/corrupt.sas7bdat
new file mode 100644
index 0000000000000..2941ffe3ecdf5
Binary files /dev/null and b/pandas/tests/io/sas/data/corrupt.sas7bdat differ
diff --git a/pandas/tests/io/sas/test_sas7bdat.py b/pandas/tests/io/sas/test_sas7bdat.py
index 8c14f9de9f61c..9de6ca75fd4d9 100644
--- a/pandas/tests/io/sas/test_sas7bdat.py
+++ b/pandas/tests/io/sas/test_sas7bdat.py
@@ -217,6 +217,14 @@ def test_zero_variables(datapath):
         pd.read_sas(fname)
 
 
+def test_corrupt_read(datapath):
+    # We don't really care about the exact failure, the important thing is
+    # that the resource should be cleaned up afterwards (BUG #35566)
+    fname = datapath("io", "sas", "data", "corrupt.sas7bdat")
+    with pytest.raises(AttributeError):
+        pd.read_sas(fname)
+
+
 def round_datetime_to_ms(ts):
     if isinstance(ts, datetime):
         return ts.replace(microsecond=int(round(ts.microsecond, -3) / 1000) * 1000)