Coach Brian Kelly leads Notre Dame onto the field before its 47-40 double-overtime win over No. 1 Clemson on Saturday night in South Bend, Indiana. Matt Cashore/Pool Photo via AP

SOUTH BEND, Ind. — For all that Notre Dame has accomplished in 11 seasons under Brian Kelly, the Fighting Irish at their best always seem to be just a little less than the best of the best in college football.

Wherever the line was drawn between the elite and the merely excellent programs, Notre Dame was on the wrong side.

How else to explain an 0-5 record against top-five teams and big-stage beatdowns by Alabama in the BCS championship game and Clemson in the College Football Playoff?

The breakthrough victory finally came Saturday night, a 47-40 thriller that knocked Clemson from No. 1 in the AP Top 25 and set off a wild celebration at Notre Dame Stadium.

After it was over, Kelly said the Irish were not out to make a statement.

“Look, all the narratives that are out there and whatever is said, you know, talked about, that doesn’t help you win this game,” said Kelly, who is now 99-37 at Notre Dame. “What we’re excited about and what we’re celebrating is that we played with an incredible focus and resolve. Those are things that we work on to try to be successful and win football games.

Kelly and his players can downplay it all they want, but Notre Dame had not beaten a No. 1 team since 1993 against Florida State, and 27 years was a long time to wait for college football’s most storied program.

Beating Clemson pushed the Fighting Irish (7-0, 6-0 ACC) to No. 2 in the AP poll, their best ranking since 2012, when they reached the BCS title game unbeaten, only to get trounced by Alabama.

“We’ve got a target on our backs now,” Kelly said. “The real challenge now is to keep this football team accelerating.”

A glance at the schedule brought back memories of 1993 for Notre Dame fans.

Next up for the Irish is Boston College (5-3, 4-3). The name David Gordon most certainly rings a bell with Notre Dame fans of a certain age.

It was Gordon’s 41-yard field goal as time expired in South Bend on Nov. 20, 1993, that gave Boston College a 41-39 victory over the top-ranked Fighting Irish, a week after they knocked off No. 1 Florida State.

The upset cost Notre Dame a national championship, and a similar slip-up could give back so much of what the Fighting Irish have gained by beating Clemson.

New coach Jeff Hafley has the Eagles overachieving behind a familiar face to the Fighting Irish. BC quarterback Phil Jurkovec is a transfer from Notre Dame.

Jurkovec was stuck behind Ian Book, who had maybe the game of his career against Clemson. The fifth-year senior threw for 310 yards and a game-tying touchdown with 22 seconds left in regulation, and also ran for 67 yards.

“Coach Kelly came up to me and said this is your game to win,” Book said. “It’s a night I’m never going to forget. Obviously, we have to go play a really good team next week. You enjoy that win tonight … but starting tomorrow, we have a new opponent.”

While Book and Kyren Williams (140 yards and three touchdowns) operated efficiently behind one of the best offensive lines in the country, Notre Dame’s defense made the difference-making plays that elite teams always seem to make against the Irish.

Jeremiah Owusu-Koramoah returned a fumble 23 yards for a touchdown in the second quarter and forced another fumble on the next possession to set up a field goal.

In the second overtime, Notre Dame sacked Clemson’s DJ Uiagalelei on consecutive plays to practically seal the victory.

Kelly, who grew up a Fighting Irish fan outside Boston, is well aware of the rivalry with the Eagles.

He is 6-0 against Boston College as Notre Dame’s coach, including a 40-7 victory last November in South Bend. A victory Saturday would be his 100th at Notre Dame, tying him with Lou Holtz, the last Irish coach to win a national title, and just behind Knute Rockne’s 105.

“We got so much more work to do,” Kelly said. “Boston College is going to be a challenge for us. I’ve got to get this football team back up, emotionally ready to play.”