The 'fixed' OP will nevertherless continue running through items 11 thru millions and test against $c for all those iterations. How about using 'last' to get out of the loop when the job is done. I also rearranged the condition handling for brevity:

$NumOfPortsToGet = 10;
$c = 0;
foreach $key (sort {$Stats{$a} <=> $Stats{$b}} keys %Stats) {
    ( $c < $NumOfPortsToGet ) or last;
    ($key eq "UnauthOrigin") or $Ports[$c++] = $key;
}
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