The Blue Devils (2-2) surpassed their previous scoring average of 18.3 points per game with 21 in the first quarter, when Thompson rushed for both of his touchdowns.
Quarterback Sean Renfree completed 21 of 30 passes for 278 yards and a touchdown for the Blue Devils. His 7-yard scramble late in the third quarter gave Duke a 45-13 lead.
Duke outgained the Green Wave (2-2) 336 yards to 127 in the first half. The only touchdown until the fourth quarter for Tulane, which scored 49 points last week in a win over UAB, came on Ryan Travis' 23-yard interception return in the first quarter.
Duke's defense, which shut out Boston College in the second half of a 20-19 win last week, had put together a streak of five quarters without allowing a touchdown.