In the still of a balmy Saturday in Palo Alto, USC linebacker John Houston made a first-half play he’ll remember for some time. Stanford’s Christian McCaffrey was flying through the air against a goal-line defense, needing just one yard to score, and Houston stopped him cold with a pretty nice Ray Lewis impression.

It requires more than a moment or two, however, to make a lasting impression. McCaffrey took it home on the very next play, his drive for the Heisman Trophy gained steam, and Stanford never felt seriously threatened in a 27-10 win. For those who have watched this rivalry unfold over the decades, it remains a bit stunning to see the Trojans so thoroughly outplayed.

They have the athletes; that’s never been in question. Too often, though, they look like the program that changes head coaches with frantic regularity. Stanford gives you the ever-solid presence of David Shaw, the magnificence of McCaffrey, and the look of a team very much in the running for this year’s four-team national playoff.

So much was to be learned this day and evening, the pundits claimed, and so it would be. The Trojans had to arrive in vintage form — think Reggie Bush, Lynn Swann, Ronnie Lott — or go 1-2 and be dismissed from relevant conversation. Stanford, derided for a so-so second half in its opening win over Kansas State, needed and delivered an upgrade commensurate with the competition.

However USC may have regressed, there’s nothing like a commanding victory over the Trojans to stir the souls of Northern California fans. Stanford alums will be toasting this one for days on end. One play, in particular, will be remembered for its defining quality.

If you’re playing Stanford, who’s the one offensive player who must be monitored on every single play? Easy answer. And yet, when McCaffrey sprinted out of the backfield and down the left sideline in the second quarter, he was left alone. Adoree’ Jackson, the Trojans’ mercurial defensive back, followed Michael Rector over the middle and he had no backup. Quarterback Ryan Burns made the easy connection to McCaffrey for a 56-yard touchdown to open the scoring, and you could almost hear the shouts of outrage from USC coaches in the press box.

It could have been even more embarrassing. McCaffrey lined up as a wide receiver in the second quarter, marked only by strong safety Chris Hawkins. With a stop-and-go move that would have made Jerry Rice proud, McCaffrey blew past Hawkins and into the wide-open spaces, but Burns’ overthrow cost Stanford an easy touchdown.

Not that the disappointment lingered. The Cardinal’s dominance was comprehensive, on both sides of the ball and right down to the backup placekicker. Punter Jake Bailey steps in for Conrad Ukropina on the kickoffs, and he launched one 73 yards (that’s eight yards deep in the end zone) for a third-quarter touchback that left Jackson standing in place as it soared over his head.

McCaffrey, meanwhile, has reached the stage in which a performance of 200-plus all-purpose yards (260 this time) is strictly routine. And the historical comparisons keep coming, from all angles.

Before the game I ran into a football-wise friend, Marc Arnett, whose name might sound familiar to USC fans. His uncle, Jon, was a storied back for USC and the Los Angeles Rams in the 1950s and early ’60s, famous for his spectacularly entertaining long-distance forays. Marc said he’d heard from Jon, who called McCaffrey “one of the best backs I’ve ever seen — and his vision of the field is unlike anyone’s I’ve seen.”

USC’s postgame news conference was a drab, three-man affair featuring coach Clay Helton, quarterback Max Browne and linebacker Cam Smith, none willing to give Stanford too much credit. That’s not surprising for a proud, tradition-laden program now struggling to get anywhere near the Cardinal’s level.

Smith said McCaffrey was “exactly what we expected.” Helton properly focused on the Trojans’ mistakes, particularly seven first-half penalties (four false starts in the first quarter alone), “and that put us in a tough position to run the ball, which is what we like to do,” he said.

So how about that battle of the bands? Stanford’s, in a runaway. The USC contingent, after boring everyone to exasperation with its endless repetition of an old theme (I believe it’s called “The Monotony of Tedium”), sought any brand of solace on its way toward the exits, chanting “Beat the Utes.”

That would be Utah, next week. Several visions come to mind there, mostly suggesting relief for USC, for none of them call to mind an unstoppable, red-clad running back wearing No. 5.

Bruce Jenkins is a San Francisco Chronicle columnist. Email: bjenkins@sfchronicle.com Twitter: @Bruce_Jenkins1