It doesn't matter how much time is on the clock when you win, as long as you have more points then the opponent.
It does matter in terms of power rankings. If on a a neutral field you think the Saints would win >50% of the time it makes sense to put them ahead of the Pats in the Power Ranking.
Given they barely pulled out a win at home and lost some key players to injury it is not unreasonable to make that determination.