To secure sensitive information such as connection strings in an AWS-based application, developers can use the AWS Key Management Service (KMS) to encrypt environment variables. This approach ensures that even if unauthorized users gain access to the codebase or AWS account, they cannot access the encrypted data. The process involves creating a Lambda function, setting up environment variables with KMS encryption, and updating the code to decrypt the connection string using the KMS key. By following these steps, developers can significantly improve the security of their applications built on AWS.