Capture::Tiny seems to handle it fine.

use Capture::Tiny qw( capture_stdout );

open STDOUT, '>/dev/tty' or die $!;

my $output = capture_stdout { print "Hello world!\n"; };

print "<<<$output>>>\n";
[download]

...the output...

<<<Hello world!
>>>
[download]

(as expected)

Update: ww has kindly reminded me that this is probably not a solution when you need to capture output of an external script. Apologies... and good luck! ;)