diff --git a/.cspell.json b/.cspell.json
index ffe51471848e..91dc7f910d0f 100644
--- a/.cspell.json
+++ b/.cspell.json
@@ -150,6 +150,7 @@
     "oxlint",
     "packagespecifier",
     "parameterised",
+    "parenthesization",
     "performant",
     "pluggable",
     "postprocess",
diff --git a/packages/eslint-plugin/src/rules/no-floating-promises.ts b/packages/eslint-plugin/src/rules/no-floating-promises.ts
index 32ecbe741681..b040d1c82122 100644
--- a/packages/eslint-plugin/src/rules/no-floating-promises.ts
+++ b/packages/eslint-plugin/src/rules/no-floating-promises.ts
@@ -1,16 +1,17 @@
 import type { TSESLint, TSESTree } from '@typescript-eslint/utils';
+import type * as ts from 'typescript';
 
 import { AST_NODE_TYPES } from '@typescript-eslint/utils';
 import * as tsutils from 'ts-api-utils';
-import * as ts from 'typescript';
 
 import type { TypeOrValueSpecifier } from '../util';
 
 import {
   createRule,
-  getOperatorPrecedence,
+  getOperatorPrecedenceForNode,
   getParserServices,
   isBuiltinSymbolLike,
+  isParenthesized,
   OperatorPrecedence,
   readonlynessOptionsDefaults,
   readonlynessOptionsSchema,
@@ -168,10 +169,11 @@ export default createRule<Options, MessageId>({
                 {
                   messageId: 'floatingFixVoid',
                   fix(fixer): TSESLint.RuleFix | TSESLint.RuleFix[] {
-                    const tsNode = services.esTreeNodeToTSNodeMap.get(
-                      node.expression,
-                    );
-                    if (isHigherPrecedenceThanUnary(tsNode)) {
+                    if (
+                      isParenthesized(expression, context.sourceCode) ||
+                      getOperatorPrecedenceForNode(expression) >
+                        OperatorPrecedence.Unary
+                    ) {
                       return fixer.insertTextBefore(node, 'void ');
                     }
                     return [
@@ -223,8 +225,10 @@ export default createRule<Options, MessageId>({
           'await',
         );
       }
-      const tsNode = services.esTreeNodeToTSNodeMap.get(node.expression);
-      if (isHigherPrecedenceThanUnary(tsNode)) {
+      if (
+        isParenthesized(expression, context.sourceCode) ||
+        getOperatorPrecedenceForNode(expression) > OperatorPrecedence.Unary
+      ) {
         return fixer.insertTextBefore(node, 'await ');
       }
       return [
@@ -261,14 +265,6 @@ export default createRule<Options, MessageId>({
       );
     }
 
-    function isHigherPrecedenceThanUnary(node: ts.Node): boolean {
-      const operator = ts.isBinaryExpression(node)
-        ? node.operatorToken.kind
-        : ts.SyntaxKind.Unknown;
-      const nodePrecedence = getOperatorPrecedence(node.kind, operator);
-      return nodePrecedence > OperatorPrecedence.Unary;
-    }
-
     function isAsyncIife(node: TSESTree.ExpressionStatement): boolean {
       if (node.expression.type !== AST_NODE_TYPES.CallExpression) {
         return false;
diff --git a/packages/eslint-plugin/src/util/getOperatorPrecedence.ts b/packages/eslint-plugin/src/util/getOperatorPrecedence.ts
index 950708015d89..54b40af26e28 100644
--- a/packages/eslint-plugin/src/util/getOperatorPrecedence.ts
+++ b/packages/eslint-plugin/src/util/getOperatorPrecedence.ts
@@ -198,6 +198,10 @@ export enum OperatorPrecedence {
   Invalid = -1,
 }
 
+/**
+ * Note that this does not take into account parenthesization. You should check
+ * for parenthesization separately if it's relevant to your usage.
+ */
 export function getOperatorPrecedenceForNode(
   node: TSESTree.Node,
 ): OperatorPrecedence {
diff --git a/packages/eslint-plugin/tests/rules/no-floating-promises.test.ts b/packages/eslint-plugin/tests/rules/no-floating-promises.test.ts
index e2a272f6f3dc..87ead2f2b19d 100644
--- a/packages/eslint-plugin/tests/rules/no-floating-promises.test.ts
+++ b/packages/eslint-plugin/tests/rules/no-floating-promises.test.ts
@@ -2044,7 +2044,7 @@ async function test() {
               messageId: 'floatingFixVoid',
               output: `
 async function test() {
-  void ((Promise.resolve(), 123));
+  void (Promise.resolve(), 123);
   (123, Promise.resolve());
   (123, Promise.resolve(), 123);
 }
@@ -2054,7 +2054,7 @@ async function test() {
               messageId: 'floatingFixAwait',
               output: `
 async function test() {
-  await ((Promise.resolve(), 123));
+  await (Promise.resolve(), 123);
   (123, Promise.resolve());
   (123, Promise.resolve(), 123);
 }
@@ -2071,7 +2071,7 @@ async function test() {
               output: `
 async function test() {
   (Promise.resolve(), 123);
-  void ((123, Promise.resolve()));
+  void (123, Promise.resolve());
   (123, Promise.resolve(), 123);
 }
       `,
@@ -2081,7 +2081,7 @@ async function test() {
               output: `
 async function test() {
   (Promise.resolve(), 123);
-  await ((123, Promise.resolve()));
+  await (123, Promise.resolve());
   (123, Promise.resolve(), 123);
 }
       `,
@@ -2098,7 +2098,7 @@ async function test() {
 async function test() {
   (Promise.resolve(), 123);
   (123, Promise.resolve());
-  void ((123, Promise.resolve(), 123));
+  void (123, Promise.resolve(), 123);
 }
       `,
             },
@@ -2108,7 +2108,7 @@ async function test() {
 async function test() {
   (Promise.resolve(), 123);
   (123, Promise.resolve());
-  await ((123, Promise.resolve(), 123));
+  await (123, Promise.resolve(), 123);
 }
       `,
             },
@@ -2237,7 +2237,7 @@ async function returnsPromise() {
 async function returnsPromise() {
   return 'value';
 }
-await ((1, returnsPromise()));
+await (1, returnsPromise());
       `,
             },
           ],
@@ -4556,13 +4556,13 @@ await promiseIntersection.finally(() => {});
             {
               messageId: 'floatingFixVoid',
               output: `
-void ((Promise.resolve().finally(() => {}), 123));
+void (Promise.resolve().finally(() => {}), 123);
       `,
             },
             {
               messageId: 'floatingFixAwait',
               output: `
-await ((Promise.resolve().finally(() => {}), 123));
+await (Promise.resolve().finally(() => {}), 123);
       `,
             },
           ],