First, I would say that we have yet to play a perfect game, or even a near-perfect game, on both sides of the ball for 60 minutes in the Saban era.
As far as the "most perfect" game in the Saban era, though, I think it's a tie between the NC games against LSU and ND.
Against LSU, the Defense - and Special Teams, for that matter - played about as perfectly as a unit can play and pitched a shutout. The Offense, however, left a bit to be desired and quite a few points on the field - albeit against a stellar Defense, which has to be considered.
Against ND, the Special Teams were once again excellent but the Defense gave up a few more big plays, 14 more points, and a lot more yards - albeit against a much better, more explosive Offense than LSU's from the previous year. The Offense, however, played about as perfectly as a unit can play and really could have named their score against what was considered to be an excellent Defense coming into the game. Also, if I remember correctly, some stats guys who track some very detailed Quarterback metrics for their own QB rating - much more detailed and accurately indicative of the quality of play than either the NCAA or NFL Passing Efficiency Rating - said that AJ's performance in that game garnered the highest rating they've ever seen in a College game (though, granted, they primarily analyze NFL games).
If you were to take the Defensive performance from the LSU NC game and combine that with the Offensive performance of the ND NC game - with a pick'em on Special Teams - then you would have as close to a perfect game as you could ever see, especially on the College level.
