A small suggestion would be adding one more slot to the buffer and using some perl idiomcyncracies (sic) to reduce the need to manipulate the buffer in the inner loop:

#!/usr/bin/env perl
use Modern::Perl;

my $lb = 3; # lookback
my $match = qr/\wiz/;
my @buff;

while ($buff[$.%($lb+1)] = ($_ = <DATA>)) {
    my $lbi = ($.+1)%($lb+1); # lookback index
    print $buff[$lbi] if defined $buff[$lbi] and /$match/;
}

__DATA__
foo
bar
baz
biz
buz
goo
car
caz
ciz
cuz
[download]

P.S. Thanks for optimizing my two line circular linked list declaration to zero lines! ;-)

P.P.S. Too bad: Yours is, IMHO, the best answer to the OP, but is buried in this subthread.

EDIT Just reviewed this code and saw that I forgot defined! This opens the door for error if the lookback line is empty or a zero. While I was at it, I changed the emphasis from the lookback line itself to the index that finds it; plus, no more relying on side effects in the conditional.

For the three of y'all who upvoted the earlier incarnation, the original code is below. One line was deleted, one line added, one line changed.

my $lbl; # lookback line
while ($buff[$.%($lb+1)] = ($_ = <DATA>)) {
    print $lbl if $lbl = $buff[($.+1)%($lb+1)] and /$match/;
}
[download]