diff --git a/release-notes/VERSION-2.x b/release-notes/VERSION-2.x
index 0273be4bae..dedd2b4f74 100644
--- a/release-notes/VERSION-2.x
+++ b/release-notes/VERSION-2.x
@@ -14,6 +14,11 @@ JSON library.
 === Releases ===
 ------------------------------------------------------------------------
 
+2.13.1 (not yet released)
+
+#713: Incorrect parsing of single-quoted surrounded String values containing double quotes
+ (reported by wcarmon@github)
+
 2.13.0 (30-Sep-2021)
 
 #652: Misleading exception for input source when processing byte buffer
diff --git a/src/main/java/com/fasterxml/jackson/core/json/ReaderBasedJsonParser.java b/src/main/java/com/fasterxml/jackson/core/json/ReaderBasedJsonParser.java
index 5d0d9b9b34..da788986c6 100644
--- a/src/main/java/com/fasterxml/jackson/core/json/ReaderBasedJsonParser.java
+++ b/src/main/java/com/fasterxml/jackson/core/json/ReaderBasedJsonParser.java
@@ -2022,10 +2022,9 @@ protected JsonToken _handleApos() throws IOException
             int i = (int) c;
             if (i <= '\\') {
                 if (i == '\\') {
-                    /* Although chars outside of BMP are to be escaped as
-                     * an UTF-16 surrogate pair, does that affect decoding?
-                     * For now let's assume it does not.
-                     */
+                    // Although chars outside of BMP are to be escaped as
+                    // an UTF-16 surrogate pair, does that affect decoding?
+                    // For now let's assume it does not.
                     c = _decodeEscaped();
                 } else if (i <= '\'') {
                     if (i == '\'') {
diff --git a/src/main/java/com/fasterxml/jackson/core/json/UTF8DataInputJsonParser.java b/src/main/java/com/fasterxml/jackson/core/json/UTF8DataInputJsonParser.java
index 58c1bebb6a..3d2fd99777 100644
--- a/src/main/java/com/fasterxml/jackson/core/json/UTF8DataInputJsonParser.java
+++ b/src/main/java/com/fasterxml/jackson/core/json/UTF8DataInputJsonParser.java
@@ -2152,7 +2152,10 @@ protected JsonToken _handleApos() throws IOException
                     if (c == '\'') {
                         break main_loop;
                     }
-                    if (codes[c] != 0) {
+                    if ((codes[c] != 0)
+                        // 13-Oct-2021, tatu: [core#721] Alas, regular quote is included as
+                        //    special, need to ignore here
+                            && (c != INT_QUOTE)) {
                         break ascii_loop;
                     }
                     outBuf[outPtr++] = (char) c;
diff --git a/src/main/java/com/fasterxml/jackson/core/json/UTF8StreamJsonParser.java b/src/main/java/com/fasterxml/jackson/core/json/UTF8StreamJsonParser.java
index 9f30ce4f43..5ad5502d63 100644
--- a/src/main/java/com/fasterxml/jackson/core/json/UTF8StreamJsonParser.java
+++ b/src/main/java/com/fasterxml/jackson/core/json/UTF8StreamJsonParser.java
@@ -2180,7 +2180,7 @@ protected String _parseAposName() throws IOException
                 break;
             }
             // additional check to skip handling of double-quotes
-            if ((codes[ch] != 0) && (ch != '"')) {
+            if ((codes[ch] != 0) && (ch != INT_QUOTE)) {
                 if (ch != '\\') {
                     // Unquoted white space?
                     // As per [JACKSON-208], call can now return:
@@ -2770,18 +2770,19 @@ protected JsonToken _handleApos() throws IOException
                 }
                 while (_inputPtr < max) {
                     c = (int) inputBuffer[_inputPtr++] & 0xFF;
-                    if (c == INT_APOS || codes[c] != 0) {
+                    if (c == INT_APOS) {
+                        break main_loop;
+                    }
+                    if ((codes[c] != 0)
+                        // 13-Oct-2021, tatu: [core#721] Alas, regular quote is included as
+                        //    special, need to ignore here
+                            && (c != INT_QUOTE)) {
                         break ascii_loop;
                     }
                     outBuf[outPtr++] = (char) c;
                 }
             }
 
-            // Ok: end marker, escape or multi-byte?
-            if (c == INT_APOS) {
-                break main_loop;
-            }
-
             switch (codes[c]) {
             case 1: // backslash
                 c = _decodeEscaped();
diff --git a/src/test/java/com/fasterxml/jackson/core/read/NonStandardAposQuotedNamesTest.java b/src/test/java/com/fasterxml/jackson/core/read/NonStandardAposQuotedNamesTest.java
index 89613a9195..619cd90f57 100644
--- a/src/test/java/com/fasterxml/jackson/core/read/NonStandardAposQuotedNamesTest.java
+++ b/src/test/java/com/fasterxml/jackson/core/read/NonStandardAposQuotedNamesTest.java
@@ -167,4 +167,62 @@ private void _testSingleQuotesEscaped(int mode) throws Exception
         assertToken(JsonToken.END_ARRAY, p.nextToken());
         p.close();
     }
+
+    // [core#721]: specific issue with enclosed unescaped double quotes
+    public void testSingleQuotedKeys721() throws Exception
+    {
+        // empty
+        _testSingleQuotedKeys721("{ '\"\"': 'value'}", "\"\"");
+        // non-empty
+        _testSingleQuotedKeys721("{ '\"key\"': 'value'}", "\"key\"");
+    }
+
+    private void _testSingleQuotedKeys721(String doc, String expKey) throws Exception
+    {
+        _testSingleQuotedKeys721(MODE_READER, doc, expKey);
+        _testSingleQuotedKeys721(MODE_INPUT_STREAM, doc, expKey);
+        _testSingleQuotedKeys721(MODE_INPUT_STREAM_THROTTLED, doc, expKey);
+        _testSingleQuotedKeys721(MODE_DATA_INPUT, doc, expKey);
+    }
+
+    private void _testSingleQuotedKeys721(int mode, String doc, String expKey) throws Exception
+    {
+        JsonParser p = createParser(APOS_F, mode, doc);
+
+        assertToken(JsonToken.START_OBJECT, p.nextToken());
+        assertEquals(expKey, p.nextFieldName());
+        assertToken(JsonToken.VALUE_STRING, p.nextToken());
+        assertEquals("value", p.getText());
+        assertToken(JsonToken.END_OBJECT, p.nextToken());
+        p.close();
+    }
+
+    // [core#721]: specific issue with enclosed unescaped double quotes
+    public void testSingleQuotedValues721() throws Exception
+    {
+        // empty
+        _testSingleQuotedValues721("{ \"bar\": '\"\"'}", "\"\"");
+        // non-empty
+        _testSingleQuotedValues721("{ \"bar\": '\"stuff\"'}", "\"stuff\"");
+    }
+
+    private void _testSingleQuotedValues721(String doc, String expValue) throws Exception
+    {
+        _testSingleQuotedValues721(MODE_READER, doc, expValue);
+        _testSingleQuotedValues721(MODE_INPUT_STREAM, doc, expValue);
+        _testSingleQuotedValues721(MODE_INPUT_STREAM_THROTTLED, doc, expValue);
+        _testSingleQuotedValues721(MODE_DATA_INPUT, doc, expValue);
+    }
+
+    private void _testSingleQuotedValues721(int mode, String doc, String expValue) throws Exception
+    {
+        JsonParser p = createParser(APOS_F, mode, doc);
+
+        assertToken(JsonToken.START_OBJECT, p.nextToken());
+        assertEquals("bar", p.nextFieldName());
+        assertToken(JsonToken.VALUE_STRING, p.nextToken());
+        assertEquals(expValue, p.getText());
+        assertToken(JsonToken.END_OBJECT, p.nextToken());
+        p.close();
+    }
 }