diff --git a/packages/core-js/internals/regexp-exec.js b/packages/core-js/internals/regexp-exec.js
index a9a0c57ff851..9eae2c437b4e 100644
--- a/packages/core-js/internals/regexp-exec.js
+++ b/packages/core-js/internals/regexp-exec.js
@@ -11,17 +11,20 @@ var nativeReplace = String.prototype.replace;
 var patchedExec = nativeExec;
 
 var LAST_INDEX = 'lastIndex';
-
-var UPDATES_LAST_INDEX_NON_GLOBAL = (function () {
-  var re = /a/;
-  nativeExec.call(re, 'a');
-  return re[LAST_INDEX] !== 0;
+var LENGTH = 'length';
+
+var UPDATES_LAST_INDEX_WRONG = (function () {
+  var re1 = /a/,
+      re2 = /b*/g;
+  nativeExec.call(re1, 'a');
+  nativeExec.call(re2, 'a');
+  return re1[LAST_INDEX] !== 0 || re2[LAST_INDEX] !== 0;
 })();
 
 // nonparticipating capturing group, copied from es5-shim's String#split patch.
 var NPCG_INCLUDED = /()??/.exec('')[1] !== undefined;
 
-var patch = UPDATES_LAST_INDEX_NON_GLOBAL || NPCG_INCLUDED;
+var patch = UPDATES_LAST_INDEX_WRONG || NPCG_INCLUDED;
 
 if (patch) {
   patchedExec = function exec(str) {
@@ -31,17 +34,19 @@ if (patch) {
     if (NPCG_INCLUDED) {
       reCopy = new RegExp('^' + re.source + '$(?!\\s)', regexpFlags.call(re));
     }
-    if (UPDATES_LAST_INDEX_NON_GLOBAL) lastIndex = this[LAST_INDEX];
+    if (UPDATES_LAST_INDEX_WRONG) lastIndex = re[LAST_INDEX];
 
-    match = nativeExec.call(this, str);
+    match = nativeExec.call(re, str);
 
-    if (UPDATES_LAST_INDEX_NON_GLOBAL && !this.global) this[LAST_INDEX] = lastIndex;
-    if (NPCG_INCLUDED && match && match.length > 1) {
+    if (UPDATES_LAST_INDEX_WRONG && match) {
+      re[LAST_INDEX] = re.global ? match.index + match[0][LENGTH] : lastIndex;
+    }
+    if (NPCG_INCLUDED && match && match[LENGTH] > 1) {
       // Fix browsers whose `exec` methods don't consistently return `undefined`
       // for NPCG, like IE8. NOTE: This doesn' work for /(.?)?/
       // eslint-disable-next-line no-loop-func
       nativeReplace.call(match[0], reCopy, function () {
-        for (i = 1; i < arguments.length - 2; i++) {
+        for (i = 1; i < arguments[LENGTH] - 2; i++) {
           if (arguments[i] === undefined) match[i] = undefined;
         }
       });
diff --git a/packages/core-js/modules/es.string.split.js b/packages/core-js/modules/es.string.split.js
index 23d56a372bb3..878219225c08 100644
--- a/packages/core-js/modules/es.string.split.js
+++ b/packages/core-js/modules/es.string.split.js
@@ -47,8 +47,7 @@ require('../internals/fix-regexp-well-known-symbol-logic')(
         var separatorCopy = new RegExp(separator.source, flags + 'g');
         var match, lastIndex, lastLength;
         while (match = regexpExec.impl.call(separatorCopy, string)) {
-          // `separatorCopy.lastIndex` is not reliable cross-browser
-          lastIndex = match.index + match[0][LENGTH];
+          lastIndex = separatorCopy.lastIndex;
           if (lastIndex > lastLastIndex) {
             output.push(string.slice(lastLastIndex, match.index));
             if (match[LENGTH] > 1 && match.index < string[LENGTH]) arrayPush.apply(output, match.slice(1));
diff --git a/tests/tests/es.regexp.exec.js b/tests/tests/es.regexp.exec.js
index fc3a9e8f17df..fd9222a01373 100644
--- a/tests/tests/es.regexp.exec.js
+++ b/tests/tests/es.regexp.exec.js
@@ -8,6 +8,14 @@ QUnit.test('RegExp#exec lastIndex updating', assert => {
   assert.strictEqual(re.lastIndex, 0, '.lastIndex starts at 0 for global regexps');
   re.exec('abc');
   assert.strictEqual(re.lastIndex, 2, '.lastIndex is updated for global regexps');
+
+  re = /b*/;
+  re.exec('a');
+  assert.strictEqual(re.lastIndex, 0, '.lastIndex isn\'t updated for non-global regexps if the match is empty');
+
+  re = /b*/g;
+  re.exec('a');
+  assert.strictEqual(re.lastIndex, 0, '.lastIndex isn\'t updated for global regexps if the match is empty');
 });
 
 QUnit.test('RegExp#exec capturing groups', assert => {