The significance of using DNSSEC (Domain Name System Security Extensions) in managing domain names lies in its ability to protect against various attacks, such as cache poisoning. DNSSEC adds a layer of security by enabling data verification during the domain name resolution process. This means that users can be more confident that the responses they receive from DNS queries are authentic and have not been altered in transit. By preventing unauthorized domain redirection, DNSSEC enhances trust in online transactions and improves overall internet security.