$DBH->do("BEGIN");  #  explicitly start a new transaction
                    #  this overrides autocommit setting
# ...
$DBH->do("COMMIT");  #end transaction, this is the "expensive part" timewise

##</code><code>##

my $dbh=DBI->connect('dbi:...', 'user', 'pass', { RaiseError => 1, AutoCommit => 1, ... });
$dbh->begin_work(); # if this fails, you have tried to nest transactions.
unless (
    eval {
        change_some_stuff($dbh);
        change_more_stuff($dbh);
        $dbh->commit();
        1;
    }
) {
    warn "Rolling back because: $@";
    eval { $dbh->rollback() };
}
# At this point, either all changes or no changes have happened in the database.