diff --git a/packages/polyfills/CHANGELOG.md b/packages/polyfills/CHANGELOG.md
index e39b4dbc0b..32e1e79511 100644
--- a/packages/polyfills/CHANGELOG.md
+++ b/packages/polyfills/CHANGELOG.md
@@ -7,6 +7,8 @@ and adheres to [Semantic Versioning](http://semver.org/spec/v2.0.0.html).
 
 <!-- ## [Unreleased] -->
 
+- Replace deprecated `babel-polyfills` in favor of `core-js` and `regenerator-runtime`. [#1660](https://github.com/Shopify/quilt/pull/1660)
+
 ## [1.2.4] - 2020-10-20
 
 - Updated `tslib` dependency to `^1.14.1`. [#1657](https://github.com/Shopify/quilt/pull/1657)
diff --git a/packages/polyfills/package.json b/packages/polyfills/package.json
index 668b1ce37e..550746569a 100644
--- a/packages/polyfills/package.json
+++ b/packages/polyfills/package.json
@@ -24,15 +24,16 @@
   },
   "homepage": "https://github.com/Shopify/quilt/blob/master/packages/polyfills/README.md",
   "dependencies": {
-    "@babel/polyfill": "^7.10.1",
     "@shopify/useful-types": "^2.2.1",
     "browser-unhandled-rejection": "^1.0.2",
     "caniuse-api": "^3.0.0",
+    "core-js": "^3.6.5",
     "formdata-polyfill": "^3.0.18",
     "intersection-observer": "^0.5.1",
     "intl-pluralrules": "^0.2.1",
     "mutationobserver-shim": "^0.3.3",
     "node-fetch": "^2.3.0",
+    "regenerator-runtime": "^0.13.7",
     "tslib": "^1.14.1",
     "url-polyfill": "^1.1.7",
     "whatwg-fetch": "^3.0.0"
diff --git a/packages/polyfills/src/base.ts b/packages/polyfills/src/base.ts
index c7c823054d..ed8a1e9d48 100644
--- a/packages/polyfills/src/base.ts
+++ b/packages/polyfills/src/base.ts
@@ -1 +1,2 @@
-require('@babel/polyfill');
+require('core-js/stable');
+require('regenerator-runtime/runtime');
diff --git a/yarn.lock b/yarn.lock
index 8000e0d47f..5f6def6cd7 100644
--- a/yarn.lock
+++ b/yarn.lock
@@ -1292,14 +1292,6 @@
     "@babel/helper-create-regexp-features-plugin" "^7.10.4"
     "@babel/helper-plugin-utils" "^7.10.4"
 
-"@babel/polyfill@^7.10.1":
-  version "7.10.1"
-  resolved "https://registry.yarnpkg.com/@babel/polyfill/-/polyfill-7.10.1.tgz#d56d4c8be8dd6ec4dce2649474e9b707089f739f"
-  integrity sha512-TviueJ4PBW5p48ra8IMtLXVkDucrlOZAIZ+EXqS3Ot4eukHbWiqcn7DcqpA1k5PcKtmJ4Xl9xwdv6yQvvcA+3g==
-  dependencies:
-    core-js "^2.6.5"
-    regenerator-runtime "^0.13.4"
-
 "@babel/preset-env@^7.10.4":
   version "7.11.5"
   resolved "https://registry.yarnpkg.com/@babel/preset-env/-/preset-env-7.11.5.tgz#18cb4b9379e3e92ffea92c07471a99a2914e4272"
@@ -5231,7 +5223,7 @@ core-js@^1.0.0:
   resolved "https://registry.yarnpkg.com/core-js/-/core-js-1.2.7.tgz#652294c14651db28fa93bd2d5ff2983a4f08c636"
   integrity sha1-ZSKUwUZR2yj6k70tX/KYOk8IxjY=
 
-core-js@^2.0.0, core-js@^2.4.0, core-js@^2.6.5:
+core-js@^2.0.0, core-js@^2.4.0:
   version "2.6.11"
   resolved "https://registry.yarnpkg.com/core-js/-/core-js-2.6.11.tgz#38831469f9922bded8ee21c9dc46985e0399308c"
   integrity sha512-5wjnpaT/3dV+XB4borEsnAYQchn00XSgTAWKDkEqv+K8KevjbzmofK6hfJ9TZIlpj2N0xQpazy7PiRQiWHqzWg==
@@ -12165,6 +12157,11 @@ regenerator-runtime@^0.13.4:
   resolved "https://registry.yarnpkg.com/regenerator-runtime/-/regenerator-runtime-0.13.5.tgz#d878a1d094b4306d10b9096484b33ebd55e26697"
   integrity sha512-ZS5w8CpKFinUzOwW3c83oPeVXoNsrLsaCoLtJvAClH135j/R77RuymhiSErhm2lKcwSCIpmvIWSbDkIfAqKQlA==
 
+regenerator-runtime@^0.13.7:
+  version "0.13.7"
+  resolved "https://registry.yarnpkg.com/regenerator-runtime/-/regenerator-runtime-0.13.7.tgz#cac2dacc8a1ea675feaabaeb8ae833898ae46f55"
+  integrity sha512-a54FxoJDIr27pgf7IgeQGxmqUNYrcV338lf/6gH456HZ/PhX+5BcwHXG9ajESmwe6WRO0tAzRUrRmNONWgkrew==
+
 regenerator-transform@^0.14.2:
   version "0.14.5"
   resolved "https://registry.yarnpkg.com/regenerator-transform/-/regenerator-transform-0.14.5.tgz#c98da154683671c9c4dcb16ece736517e1b7feb4"