diff --git a/lib/rules/no-deprecated-dollar-listeners-api.js b/lib/rules/no-deprecated-dollar-listeners-api.js
index 29c0655d0..b833b462b 100644
--- a/lib/rules/no-deprecated-dollar-listeners-api.js
+++ b/lib/rules/no-deprecated-dollar-listeners-api.js
@@ -50,11 +50,19 @@ module.exports = {
       },
       utils.defineVueVisitor(context,
         {
-          'MemberExpression > ThisExpression' (node) {
-            if (node.parent.property.name !== '$listeners') return
+          'MemberExpression' (node) {
+            if (
+              node.property.type !== 'Identifier' ||
+              node.property.name !== '$listeners'
+            ) {
+              return
+            }
+            if (!utils.isThis(node.object, context)) {
+              return
+            }
 
             context.report({
-              node: node.parent.property,
+              node: node.property,
               messageId: 'deprecated'
             })
           }
diff --git a/lib/rules/no-deprecated-events-api.js b/lib/rules/no-deprecated-events-api.js
index 8537469ee..7989ffb5e 100644
--- a/lib/rules/no-deprecated-events-api.js
+++ b/lib/rules/no-deprecated-events-api.js
@@ -32,11 +32,21 @@ module.exports = {
   create (context) {
     return utils.defineVueVisitor(context,
       {
-        'CallExpression > MemberExpression > ThisExpression' (node) {
-          if (!['$on', '$off', '$once'].includes(node.parent.property.name)) return
+        'CallExpression > MemberExpression' (node) {
+          const call = node.parent
+          if (
+            call.callee !== node ||
+            node.property.type !== 'Identifier' ||
+            !['$on', '$off', '$once'].includes(node.property.name)
+          ) {
+            return
+          }
+          if (!utils.isThis(node.object, context)) {
+            return
+          }
 
           context.report({
-            node: node.parent.parent,
+            node: node.property,
             messageId: 'noDeprecatedEventsApi'
           })
         }
diff --git a/lib/rules/require-explicit-emits.js b/lib/rules/require-explicit-emits.js
index 2addf8471..c811fc9ce 100644
--- a/lib/rules/require-explicit-emits.js
+++ b/lib/rules/require-explicit-emits.js
@@ -262,8 +262,7 @@ module.exports = {
 
           // verify $emit
           if (emit && emit.name === '$emit') {
-            const objectType = emit.member.object.type
-            if (objectType === 'Identifier' || objectType === 'ThisExpression') {
+            if (utils.isThis(emit.member.object, context)) {
               // verify this.$emit()
               verify(emitsDeclarations, nameLiteralNode, vueNode)
             }
diff --git a/lib/utils/index.js b/lib/utils/index.js
index 3e1ce4c58..c31ed0e6e 100644
--- a/lib/utils/index.js
+++ b/lib/utils/index.js
@@ -41,6 +41,7 @@ const VOID_ELEMENT_NAMES = new Set(require('./void-elements.json'))
 const assert = require('assert')
 const path = require('path')
 const vueEslintParser = require('vue-eslint-parser')
+const { findVariable } = require('eslint-utils')
 
 /**
  * @type { WeakMap<RuleContext, Token[]> }
@@ -855,7 +856,34 @@ module.exports = {
    * @param {T} node
    * @return {T}
    */
-  unwrapTypes
+  unwrapTypes,
+
+  /**
+   * Check whether the given node is `this` or variable that stores `this`.
+   * @param  {ASTNode} node The node to check
+   * @returns {boolean} `true` if the given node is `this`.
+   */
+  isThis (node, context) {
+    if (node.type === 'ThisExpression') {
+      return true
+    }
+    if (node.type !== 'Identifier') {
+      return false
+    }
+    const variable = findVariable(context.getScope(), node)
+
+    if (variable != null && variable.defs.length === 1) {
+      const def = variable.defs[0]
+      if (
+        def.parent &&
+        def.parent.kind === 'const' &&
+        def.node.id.type === 'Identifier'
+      ) {
+        return def.node && def.node.init && def.node.init.type === 'ThisExpression'
+      }
+    }
+    return false
+  }
 }
 
 /**
diff --git a/tests/lib/rules/no-deprecated-dollar-listeners-api.js b/tests/lib/rules/no-deprecated-dollar-listeners-api.js
index 76f7c73cc..98a0d6270 100644
--- a/tests/lib/rules/no-deprecated-dollar-listeners-api.js
+++ b/tests/lib/rules/no-deprecated-dollar-listeners-api.js
@@ -101,6 +101,21 @@ ruleTester.run('no-deprecated-dollar-listeners-api', rule, {
         }
         </script>
       `
+    },
+    {
+      filename: 'test.vue',
+      code: `
+        <script>
+        export default {
+          computed: {
+            foo () {
+              const {vm} = this
+              return vm.$listeners
+            }
+          }
+        }
+        </script>
+      `
     }
   ],
 
@@ -179,6 +194,53 @@ ruleTester.run('no-deprecated-dollar-listeners-api', rule, {
           endColumn: 33
         }
       ]
+    },
+    {
+      filename: 'test.vue',
+      code: `
+        <script>
+        export default {
+          computed: {
+            foo () {
+              const vm = this
+              return vm.$listeners
+            }
+          }
+        }
+        </script>
+      `,
+      errors: [
+        {
+          line: 7,
+          column: 25,
+          messageId: 'deprecated'
+        }
+      ]
+    },
+    {
+      filename: 'test.vue',
+      code: `
+        <script>
+        export default {
+          computed: {
+            foo () {
+              const vm = this
+              function fn() {
+                return vm.$listeners
+              }
+              return fn()
+            }
+          }
+        }
+        </script>
+      `,
+      errors: [
+        {
+          line: 8,
+          column: 27,
+          messageId: 'deprecated'
+        }
+      ]
     }
   ]
 })
diff --git a/tests/lib/rules/no-deprecated-events-api.js b/tests/lib/rules/no-deprecated-events-api.js
index 215a47d86..268c0a712 100644
--- a/tests/lib/rules/no-deprecated-events-api.js
+++ b/tests/lib/rules/no-deprecated-events-api.js
@@ -103,6 +103,17 @@ ruleTester.run('no-deprecated-events-api', rule, {
         }
       `,
       parserOptions
+    },
+    {
+      filename: 'test.vue',
+      code: `
+        export default {
+          mounted () {
+            a(this.$on)
+          }
+        }
+      `,
+      parserOptions
     }
   ],
 
@@ -155,6 +166,24 @@ ruleTester.run('no-deprecated-events-api', rule, {
         message: 'The Events api `$on`, `$off` `$once` is deprecated. Using external library instead, for example mitt.',
         line: 4
       }]
+    },
+    {
+      filename: 'test.js',
+      code: `
+        app.component('some-comp', {
+          mounted () {
+            const vm = this
+            vm.$on('start', function (args) {
+              console.log('start', args)
+            })
+          }
+        })
+      `,
+      parserOptions,
+      errors: [{
+        message: 'The Events api `$on`, `$off` `$once` is deprecated. Using external library instead, for example mitt.',
+        line: 5
+      }]
     }
   ]
 })