You don't need a visa assuming your bags are checked through all the way to SIN. There is also a (relatively expensive) transit hotel in T3 in case you want to sleep during that time. No visa required.

http://www.newdelhiairport.in/eaton-smart.aspx

The info from the CGI is incorrect, no visa is necessary to stay in this hotel, although it would apply at airport hotels in other cities (since none are transit hotels like this one).