But by whatever means or final score, this was an essential win against an old nemesis that had beaten Miami three consecutive times. This was a game that might easily have slipped away and dissolved into postgame excuses.

Instead, this kind of victory, on a nationally televised Thursday stage, is how a program starts to worm its way back into the sports’ broadest consciousness.

It does not erase the bad — which for Miami this season has been an 0-3 record against ranked opponents Kansas State, Notre Dame and FSU by a combined score of 126-36 — but it helps stem the bleeding. It encourages the willing to take another look.

With a 4-2 conference record, Miami is in control now to win the ACC’s Coastal Division, with both its remaining league games on the road but against weaker opponents in Virginia and Duke. Win both and the Canes are assured of being in the ACC title game in Charlotte, N.C., with the winner of that securing an automatic berth in the hometown Orange Bowl Classic right back here in this same stadium.

A top-tier BCS appearance reasonably within reach — that is what Thursday night meant.

Of course all of this is in the inescapable context of looming likely NCAA sanctions related to the mess instigated by disgraced, jailed former renegade booster Nevin Shapiro.

Last season, UM self-imposed a bowl ban, hoping that might mitigate against future penalties.

The same option is in play for the university now, still.

There is no perfect answer, but, to me, the right question is whether this team will have done enough to earn a reward.

A team that slogs to six losses and is nowhere close to its conference finale (that was UM a year ago) has not earned a reward.

A team that plays itself into a major-conference championship game — especially a team this young, playing 21 freshmen, a team not among preseason favorites — has earned that reward.

That is what Thursday night meant.

The Canes might still be a ways from repeating the glory days personified by Jimmy Johnson; lord knows the NCAA will have something to say about that.

But the map there, that road “back,” would never even have a chance without nights like this one.