What is the current code you have and how does it fail to do what you want?

Most likely it is merely a matter of putting the user and password into the URL as basic authentication elements.

use HTTP::Tiny;
my $url = 'https://<my-url>';
my $headers = {
                  Accept => "application/json",
                  'Content-Type' => "application/json",
                  Authorization => "user:password"
              };
my $response = HTTP::Tiny->new->get($url, { headers => $headers });
if ($response->{success}) {
    my $html = $response->{content};
    print "$html\n";
    }
else
{
   print "failure: $response->{status}\n";
}

This prints 401
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once when i was forced to do authorization myself (via tkx sockets) i used

  if ($args{user} || $args{password}) { 
      use MIME::Base64;
      $tkxf_auth='Authorization: Basic '.encode_base64($args{user}.':'
+.$args{password},''); 
      }
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which would make your call

use MIME::Base64;
my $headers = {
                  Accept => "application/json",
                  'Content-Type' => "application/json",
                  Authorization => 'Authorization: Basic '.encode_base
+64($args{user}.':'.$args{password},'')
              };
[download]

Edit: the real userid/passwords are stored in the hash %args under keys userid and password!

Authorization => "user:password"
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Are you sure that you want to send an "Authorization" header with exactly user:password in it?

The usual format for Authorization headers says that it has at least a type in front of it:

Authorization: <type> <credentials>
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So maybe now is the time to look at what data Curl would try to send over the network and then try to replicate that using Perl / HTTP::Tiny.