Благодаря справочному пакету от Sinan Ünür я смог выполнить то, что мне было нужно:
my $host = 'pilot-payflowpro.paypal.com';
my $port = 443;
my $sock = IO::Socket::SSL->new("$host:$port") || die $!;
my $req = 'EXPDATE[4]=1011&AMT[6]=100.01&ACCT[16]=4111111111111111&TENDER[1]=C&TAXAMT[4]=0.00&PARTNER[8]=*****&PWD[9]=******&VENDOR[6]=*****&USER[6]=******&TRXTYPE[1]=S&VERBOSITY=MEDIUM';
print $sock "POST https://$host/ HTTPS/1.1\r\n";
print $sock "Connection: close", "\r\n";
print $sock "Host: ", $host, "\r\n";
print $sock "Content-length: ", length $req, "\r\n";
print $sock "Content-type: text/namevalue\r\n";
print $sock "X-VPS-CLIENT-TIMEOUT: 30", "\r\n";
print $sock "X-VPS-REQUEST-ID: 1249403513SNOID", "\r\n";
print $sock "X-VPS-VIT-INTEGRATION-PRODUCT: Product", "\r\n";
print $sock "X-VPS-VIT-INTEGRATION-VERSION: 4.0", "\r\n";
print $sock "X-VPS-VIT-OS-NAME: linux", "\r\n";
print $sock "X-VPS-VIT-OS-VERSION: 2.6.16-gentoo-r13", "\r\n";
print $sock "X-VPS-VIT-RUNTIME-VERSION: 5.008007", "\r\n\r\n";
print $sock $req, "\r\n\r\n";
print while <$sock>;
close $sock;