diff --git a/lib/rules/quotes.js b/lib/rules/quotes.js
index 6dd0ed996c7..5c53c76908c 100644
--- a/lib/rules/quotes.js
+++ b/lib/rules/quotes.js
@@ -258,7 +258,11 @@ module.exports = {
                     return;
                 }
 
-                const shouldWarn = node.quasis.length === 1 && (node.quasis[0].value.cooked.indexOf("\n") === -1);
+                /*
+                 * A warning should be produced if the template literal only has one TemplateElement, and has no unescaped newlines.
+                 * An unescaped newline is a newline preceded by an even number of backslashes.
+                 */
+                const shouldWarn = node.quasis.length === 1 && !/(^|[^\\])(\\\\)*[\r\n\u2028\u2029]/.test(node.quasis[0].value.raw);
 
                 if (shouldWarn) {
                     context.report({
diff --git a/tests/lib/rules/quotes.js b/tests/lib/rules/quotes.js
index d01ef76cbdc..d7430c8c19c 100644
--- a/tests/lib/rules/quotes.js
+++ b/tests/lib/rules/quotes.js
@@ -38,6 +38,16 @@ ruleTester.run("quotes", rule, {
 
         // Backticks are only okay if they have substitutions, contain a line break, or are tagged
         { code: "var foo = `back\ntick`;", options: ["single"], parserOptions: { ecmaVersion: 6 }},
+        { code: "var foo = `back\rtick`;", options: ["single"], parserOptions: { ecmaVersion: 6 }},
+        { code: "var foo = `back\u2028tick`;", options: ["single"], parserOptions: { ecmaVersion: 6 }},
+        { code: "var foo = `back\u2029tick`;", options: ["single"], parserOptions: { ecmaVersion: 6 }},
+        {
+            code: "var foo = `back\\\\\ntick`;", // 2 backslashes followed by a newline
+            options: ["single"],
+            parserOptions: { ecmaVersion: 6 }
+        },
+        { code: "var foo = `back\\\\\\\\\ntick`;", options: ["single"], parserOptions: { ecmaVersion: 6 }},
+        { code: "var foo = `\n`;", options: ["single"], parserOptions: { ecmaVersion: 6 }},
         { code: "var foo = `back${x}tick`;", options: ["double"], parserOptions: { ecmaVersion: 6 }},
         { code: "var foo = tag`backtick`;", options: ["double"], parserOptions: { ecmaVersion: 6 }},
 
@@ -272,6 +282,26 @@ ruleTester.run("quotes", rule, {
             output: "foo(); \"use strict\";",
             parserOptions: { ecmaVersion: 6 },
             errors: [{ message: "Strings must use doublequote.", type: "TemplateLiteral" }]
+        },
+
+        // https://github.com/eslint/eslint/issues/7646
+        {
+            code: "var foo = `foo\\nbar`;",
+            output: "var foo = \"foo\\nbar\";",
+            parserOptions: { ecmaVersion: 6 },
+            errors: [{ message: "Strings must use doublequote.", type: "TemplateLiteral" }]
+        },
+        {
+            code: "var foo = `foo\\\nbar`;", // 1 backslash followed by a newline
+            output: "var foo = \"foo\\\nbar\";",
+            parserOptions: { ecmaVersion: 6 },
+            errors: [{ message: "Strings must use doublequote.", type: "TemplateLiteral" }]
+        },
+        {
+            code: "var foo = `foo\\\\\\\nbar`;", // 3 backslashes followed by a newline
+            output: "var foo = \"foo\\\\\\\nbar\";",
+            parserOptions: { ecmaVersion: 6 },
+            errors: [{ message: "Strings must use doublequote.", type: "TemplateLiteral" }]
         }
     ]
 });