diff --git a/spec/core/asymmetric_equality/AnythingSpec.js b/spec/core/asymmetric_equality/AnythingSpec.js
index 8ee1f4e5..f248226a 100644
--- a/spec/core/asymmetric_equality/AnythingSpec.js
+++ b/spec/core/asymmetric_equality/AnythingSpec.js
@@ -23,6 +23,22 @@ describe("Anything", function() {
     expect(anything.asymmetricMatch([1,2,3])).toBe(true);
   });
 
+  it("matches a Map", function() {
+    jasmine.getEnv().requireFunctioningMaps();
+
+    var anything = new jasmineUnderTest.Anything();
+
+    expect(anything.asymmetricMatch(new Map())).toBe(true);
+  });
+
+  it("matches a Set", function() {
+    jasmine.getEnv().requireFunctioningSets();
+
+    var anything = new jasmineUnderTest.Anything();
+
+    expect(anything.asymmetricMatch(new Set())).toBe(true);
+  });
+
   it("doesn't match undefined", function() {
     var anything = new jasmineUnderTest.Anything();
 
diff --git a/spec/core/matchers/toEqualSpec.js b/spec/core/matchers/toEqualSpec.js
index aaed7759..d1605a4f 100644
--- a/spec/core/matchers/toEqualSpec.js
+++ b/spec/core/matchers/toEqualSpec.js
@@ -504,6 +504,14 @@ describe("toEqual", function() {
     expect(compareEquals(actual, expected).message).toEqual(message);
   });
 
+  it("does not report mismatches when comparing Map key to jasmine.anything()", function() {
+    jasmine.getEnv().requireFunctioningMaps();
+
+    var actual = new Map([['a', 1]]),
+      expected = new Map([[jasmineUnderTest.anything(), 1]]);
+    expect(compareEquals(actual, expected).pass).toBe(true);
+  });
+
   function isNotRunningInBrowser() {
     return typeof document === 'undefined'
   }
diff --git a/src/core/matchers/matchersUtil.js b/src/core/matchers/matchersUtil.js
index a9801910..71fc0047 100644
--- a/src/core/matchers/matchersUtil.js
+++ b/src/core/matchers/matchersUtil.js
@@ -253,16 +253,34 @@ getJasmineRequireObj().matchersUtil = function(j$) {
         return false;
       }
 
-      // For both sets of keys, check they map to equal values in both maps
+      // For both sets of keys, check they map to equal values in both maps.
+      // Keep track of corresponding keys (in insertion order) in order to handle asymmetric obj keys.
       var mapKeys = [a.keys(), b.keys()];
-      var mapIter, mapKeyIt, mapKey;
+      var cmpKeys = [b.keys(), a.keys()];
+      var mapIter, mapKeyIt, mapKey, mapValueA, mapValueB;
+      var cmpIter, cmpKeyIt, cmpKey;
       for (i = 0; result && i < mapKeys.length; i++) {
         mapIter = mapKeys[i];
+        cmpIter = cmpKeys[i];
         mapKeyIt = mapIter.next();
+        cmpKeyIt = cmpIter.next();
         while (result && !mapKeyIt.done) {
           mapKey = mapKeyIt.value;
-          result = eq(a.get(mapKey), b.get(mapKey), aStack, bStack, customTesters, j$.NullDiffBuilder());
+          cmpKey = cmpKeyIt.value;
+          mapValueA = a.get(mapKey);
+
+          // Only use the cmpKey when one of the keys is asymmetric and the corresponding key matches,
+          // otherwise explicitly look up the mapKey in the other Map since we want keys with unique
+          // obj identity (that are otherwise equal) to not match.
+          if (isAsymmetric(mapKey) || isAsymmetric(cmpKey) &&
+              eq(mapKey, cmpKey, aStack, bStack, customTesters, j$.NullDiffBuilder())) {
+            mapValueB = b.get(cmpKey);
+          } else {
+            mapValueB = b.get(mapKey);
+          }
+          result = eq(mapValueA, mapValueB, aStack, bStack, customTesters, j$.NullDiffBuilder());
           mapKeyIt = mapIter.next();
+          cmpKeyIt = cmpIter.next();
         }
       }