The spectacular play earned the game's MVP award for Boykin, a junior receiver who caught three passes for 102 yards.
Book had replaced starting Notre Dame quarterback Brandon Wimbush late in the first half when the score was 0-0. He completed 14 of 19 passes for 164 yards and two touchdowns.
Notre Dame (10-3) won after being outgained and committing two turnovers, only one of which turned into LSU points.
Jack Gonsoulin's 17-yard field goal had given LSU (9-4) a 17-14 lead with 2:03 left.
Derrius Guice ran for 98 yards and scored both of LSU's touchdowns on short passes from Danny Etling.
The game's first turnover set up the first touchdown early in the second half, giving LSU a 7-3 lead.
A punt grazed the leg of Notre Dame's Isaiah Robertson and was recovered by LSU's Blake Ferguson at the Notre Dame 43. Guice scored five plays later on a 20-yard pass from Etling with 11:37 left in the third quarter.
LSU drove 75 yards in 12 plays to its second touchdown, which came on a 2-yard pass to Guice, putting the Tigers up 14-6 with 11:13 remaining.
That drive was sustained by a 26-yard third-down completion to tight end Foster Moreau.
Notre Dame answered with a 10-play, 75-yard drive for its first touchdown. Book found Michael Young in the back of the end zone from 6 yards, then flipped a shovel pass to Josh Adams for the two-point conversion and a 14-14 tie with 7:49 left.
Missed field goal attempts by two different kickers kept LSU off the scoreboard in the first half.
After three straight exchanges of punts, the Tigers drove 65 yards to within a foot of the Irish goal line when a false start moved them back. Connor Culp's 22-yard field goal attempt went wide right.
Etling then connected on two long third-down conversions to move the Tigers as far as the Notre Dame 10. But Gonsoulin pulled a 37-yard attempt wide to the left with two minutes left in the half.
Book took over at quarterback and drove the Irish 51 yards to a 46-yard Justin Yoon field goal for the only points of the first half.
Yoon added a 49-yard field goal in the rain to pull Notre Dame within 7-6 with 2:47 left in the third quarter.
NOTES: Of Notre Dame's 154 total yards in the first half, 35 came on Brandon Wimbush's completion to Equanimeous St. Brown on the first play from scrimmage, 31 came on a run by Wimbush, and 21 more came on Book's third-and-20 run during the drive for a field goal. ... It was the 48th bowl appearance (18th straight) for LSU and the 36th for Notre Dame, which chose not to go bowling for 45 years after its first bowl appearance in 1924. ... A crowd of 57,726 was announced.