I wouldn't use greediness at all. I'd use "Not this character" matches:

use warnings;
use strict;

my $xpath = 'BoringNode[1]/InterestingNode[@InterestingAttribute="outg
+rabe"]/AnotherBoringNode[5]';
$xpath =~ s|\/[^/]+$||;
print $xpath . "\n";
[download]

That's "any character that isn't a slash"