Is there a reason you don't use the database to join these two arrays? If you can't, you could use the following:

sub commonLists {
    my ( $array_ref1, $array_ref2, $elementToMatch ) = @_;

    my %lookup = map { $_->[$elementToMatch] => $_ } @$array_ref1;

    my @match;
    foreach my $fromArray2 (@$array_ref2) {
        my $fromArray1 = $lookup{$fromArray2->[$elementToMatch]};
        push(@match, $fromArray1, $fromArray2) if $fromArray1;
    }
    return \@match;
}
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Or if the field is not a key:

sub commonLists {
    my ( $array_ref1, $array_ref2, $elementToMatch ) = @_;

    my %lookup;
    push(@{$lookup{$_->[$elementToMatch]}}, $_)
       foreach @$array_ref1;

    my @match;
    foreach my $fromArray2 (@$array_ref2) {
        my $fromArray1 = $lookup{$fromArray2->[$elementToMatch]};
        push(@match, @$fromArray1, $fromArray2) if $fromArray1;
    }
    return \@match;
}
[download]

But it won't work until you fix the bug in your code.
my @matchedLists = &commonLists( \$array_ref1, \$array_ref2, 2 );
should be
my @matchedLists = &commonLists( \@array1, \@array2, 2 );
or
my @matchedLists = &commonLists( $array_ref1, $array_ref2, 2 );

Your variable naming stayle is inconsistent. You use both fooBar and foo_bar for similar things. Be consistent.