I don't think it was luck. They won games how NE wins a lot of games.
They didn't beat themselves, and they let the other team self destruct.
4 plays that made the difference ..
1. The sack fumble/TD
2. The INT by Jack
3. Steelers Not converting on 4th and inches
4 Steelers once again not converting on 4th and 1.
3 and 4 I listed above were just huge mental errors by Tomlin/Haley.
Tomlin also had a few questionable calls during the game, like doing the onside kick.
So I would say no it wasn't luck, it was taking advantage of mistakes by Big Ben, Tomlin, and Haley
that were ultimately the difference