diff --git a/doc/source/whatsnew/v0.24.0.txt b/doc/source/whatsnew/v0.24.0.txt
index 3e22084d98234..ade395b15cd47 100644
--- a/doc/source/whatsnew/v0.24.0.txt
+++ b/doc/source/whatsnew/v0.24.0.txt
@@ -615,6 +615,7 @@ Timezones
 - Bug when setting a new value with :meth:`DataFrame.loc` with a :class:`DatetimeIndex` with a DST transition (:issue:`18308`, :issue:`20724`)
 - Bug in :meth:`DatetimeIndex.unique` that did not re-localize tz-aware dates correctly (:issue:`21737`)
 - Bug when indexing a :class:`Series` with a DST transition (:issue:`21846`)
+- Bug in :meth:`DataFrame.resample` when :class:`DatetimeIndex` starts or ends on a DST transition (:issue:`10117`, :issue:`19375`)
 
 Offsets
 ^^^^^^^
diff --git a/pandas/_libs/tslibs/conversion.pyx b/pandas/_libs/tslibs/conversion.pyx
index fe664cf03b0b9..966801a400c37 100644
--- a/pandas/_libs/tslibs/conversion.pyx
+++ b/pandas/_libs/tslibs/conversion.pyx
@@ -893,34 +893,39 @@ def tz_localize_to_utc(ndarray[int64_t] vals, object tz, object ambiguous=None,
     tdata = <int64_t*> cnp.PyArray_DATA(trans)
     ntrans = len(trans)
 
+    # Determine whether each date lies left of the DST transition (store in
+    # result_a) or right of the DST transition (store in result_b)
     result_a = np.empty(n, dtype=np.int64)
     result_b = np.empty(n, dtype=np.int64)
     result_a.fill(NPY_NAT)
     result_b.fill(NPY_NAT)
 
-    # left side
-    idx_shifted = (np.maximum(0, trans.searchsorted(
+    idx_shifted_left = (np.maximum(0, trans.searchsorted(
         vals - DAY_NS, side='right') - 1)).astype(np.int64)
 
-    for i in range(n):
-        v = vals[i] - deltas[idx_shifted[i]]
-        pos = bisect_right_i8(tdata, v, ntrans) - 1
-
-        # timestamp falls to the left side of the DST transition
-        if v + deltas[pos] == vals[i]:
-            result_a[i] = v
-
-    # right side
-    idx_shifted = (np.maximum(0, trans.searchsorted(
+    idx_shifted_right = (np.maximum(0, trans.searchsorted(
         vals + DAY_NS, side='right') - 1)).astype(np.int64)
 
     for i in range(n):
-        v = vals[i] - deltas[idx_shifted[i]]
-        pos = bisect_right_i8(tdata, v, ntrans) - 1
-
-        # timestamp falls to the right side of the DST transition
-        if v + deltas[pos] == vals[i]:
-            result_b[i] = v
+        v_left = vals[i] - deltas[idx_shifted_left[i]]
+        if v_left in trans:
+            # The vals[i] lies directly on the DST border.
+            result_a[i] = v_left
+        else:
+            pos_left = bisect_right_i8(tdata, v_left, ntrans) - 1
+            # timestamp falls to the left side of the DST transition
+            if v_left + deltas[pos_left] == vals[i]:
+                result_a[i] = v_left
+
+        v_right = vals[i] - deltas[idx_shifted_right[i]]
+        if v_right in trans:
+            # The vals[i] lies directly on the DST border.
+            result_b[i] = v_right
+        else:
+            pos_right = bisect_right_i8(tdata, v_right, ntrans) - 1
+            # timestamp falls to the right side of the DST transition
+            if v_right + deltas[pos_right] == vals[i]:
+                result_b[i] = v_right
 
     if infer_dst:
         dst_hours = np.empty(n, dtype=np.int64)
diff --git a/pandas/tests/test_resample.py b/pandas/tests/test_resample.py
index 38801832829b0..73b48fbf511c3 100644
--- a/pandas/tests/test_resample.py
+++ b/pandas/tests/test_resample.py
@@ -2125,6 +2125,26 @@ def test_downsample_across_dst(self):
                                            freq='H'))
         tm.assert_series_equal(result, expected)
 
+    def test_bin_edges_on_DST_transition(self):
+        # GH 10117
+        # Ends on DST boundary
+        idx = date_range("2014-10-26 00:30:00", "2014-10-26 02:30:00",
+                         freq="30T", tz="Europe/London")
+        expected = Series(range(len(idx)), index=idx)
+        result = expected.resample('30T').mean()
+        tm.assert_series_equal(result, expected)
+
+        # Starts on DST boundary
+        idx = date_range('2014-03-09 03:00', periods=4,
+                         freq='H', tz='America/Chicago')
+        s = Series(range(len(idx)), index=idx)
+        result = s.resample('H', label='right', closed='right').sum()
+        expected = Series([1, 2, 3], index=date_range('2014-03-09 04:00',
+                                                      periods=3,
+                                                      freq='H',
+                                                      tz='America/Chicago'))
+        tm.assert_series_equal(result, expected)
+
     def test_resample_with_nat(self):
         # GH 13020
         index = DatetimeIndex([pd.NaT,