This has come in handy more times than it should have.

Configuration

To redirect all requests to example.com:

heroku config:add NEW_BASE_URL=http://example.com

To use an alternative HTTP status code set REDIRECT_STATUS. Defaults to 302.

heroku config:add REDIRECT_STATUS=301

Deployment

If the old app that you're redirecting from isn't a Node app you'll need to change the buildpack:

heroku buildpacks:set heroku/nodejs

You can then replace the app by pushing with -f:

git push heroku master -f

NOTE: If the above doesn't work you may need to delete and re-create your Heroku app before pushing an entirely new Git repository into it.