It will be the Blue Devils' 16th appearance in the Final Four and 12th under coach Mike Krzyzewski, matching the all-time record of UCLA's John Wooden.
Duke's last Final Four and national title was in 2010, when the Blue Devils were also the No. 1 seed in the South Regional and had to go through Houston.
No. 2 seed Gonzaga (35-3) had taken a 38-34 lead less than 4 minutes into the second half, putting the Blue Devils in their largest deficit of this tournament.
The young Blue Devils responded with nine straight points and never trailed again.
Gonzaga, in its 17th consecutive NCAA Tournament, was trying to get to the Final Four for the first time.
Kyle Wiltjer had 16 points for Gonzaga.
MICHIGAN STATE 76, LOUISVILLE 70, OT
SYRACUSE, N.Y. (AP) - Senior guard Travis Trice scored 17 points and the seventh-seeded Spartans clamped down on defense to advance to their ninth Final Four, seven under coach Tom Izzo.
The Spartans (28-11), who were nearly counted out of the tournament conversation in February, won for the 12th time in 15 games. It's a run that included them knocking off second-seeded Virginia last weekend and third-seeded Oklahoma in the regional semifinal on Friday.
Michigan State advances to face Duke, the South Regional champion.
Wayne Blackshear had 28 points for the Cardinals (27-9).
The Spartans rallied from a 40-32 halftime deficit to eventually build a 61-59 lead with 3:57 left, when Trice hit two free throws.
The Cardinals rallied and had a chance to pull out the victory in regulation. Down 65-64, Mangok Mathiang hit one of two free throws with 4.9 seconds left. Michigan State took control in overtime, starting with Bryn Forbes hitting a 3-pointer 26 seconds in.
After hitting 17 of 32 attempts in the first half, Louisville managed to make six of its final 32.