Not a coincidence that some of our best games defensively were ones where the offense controlled time of possession.
First, Time of Possession (usually) does not lead to winning, winning leads to being in a position to lead in time of possession. Time in which you have the ball is time in which you are not scoring. Sometimes possession is more important and sometimes scoring is more important, but it's an alternate possession game and you can't do both at the same time.
If you have a big time of possession advantage and are successful in the game, then you more than likely have at least a pretty good defense that day. If you have a big time of possession advantage and your defense is doing poorly, then that likely means they're scoring very fast and (if) you're scoring it is very slow. That's usually not a relationship conducive to winning because long drives are harder to sustain obviously than quick ones. Teams that want to play a clock control game have to play decent defense because with the number of drives being low the clock quickly becomes their enemy if they get too far behind.
Second, I don't think I agree that there even is a relationship in terms of Nebraska's defense and time of possession. The three lowest scoring opponents after the coaching changes were Rutgers, Wisconsin, and Iowa.
Against Rutgers, Nebraska did have a TOP advantage but the number of plays were nearly identical (66 vs 68) and Nebraska only gained 4 first downs rushing. 29 rushes for 72 yards.
Wisconsin dominated both TOP and the stats. Nebraska only gained 171 total yards that day.
Iowa makes everyone's defense looked good. Note, though, this also wasn't a game in which Nebraska controlled the clock. Yes, they led in TOP, but only 3 rushing first downs and only 51 yards on 35 carries. Iowa ran more plays (65 vs 72) but Nebraska had the bigger plays.
Indiana is the closest I would say to this relationship holding true, but under closer examination it falls flat, too. The defense held a shutout the second half, but what did the offense do? First 4 possessions of the second half:
6 plays, 19 yards, 2:33 PUNT
1 play INT
5 plays, -2 yards, 2:29 PUNT
3 plays, -5 yards, 1:46 PUNT
Nebraska does break the 21 all tie with a 71 yard bomb to Palmer, and eventually has a 12 play TD drive, but that's the only drive of the half that is in any way a ball control drive. Meanwhile, Indiana went 3 and out on nearly every drive in the second half.