Jordan Sibert led the way with 18 points and the upstart Flyers thoroughly handled Stanford, 82-72, in a Sweet 16 battle of double-digit seeds from the South Region.
Eleven different players scored in an efficiently balanced attack for the 11th-seeded Flyers (26-10), who made 48.3 percent of their shots and assisted on 19 of their 28 made baskets.
Kendall Pollard scored 12 points off the bench, Devin Oliver chipped in with 12 points and seven rebounds and Matt Kavanaugh added 10 points for Dayton, which last reached the Elite Eight of the NCAA Tournament in 1984, when they lost to Georgetown in the regional final.
They'll face another perennial power next in the winner of Thursday's nightcap at FedEx Forum between top-seeded Florida and fourth-seeded UCLA.
Stanford's leading scorer, Chasson Randle, needed 21 shots to score 21 points, and the 10th-seeded Cardinal (23-13) had three other double-digit scorers in Dwight Powell, Stefan Nastic and Josh Huestis.
Powell finished with 17 points and nine rebounds, Nastic had 15 points before fouling out and Huestis netted 13, but Stanford only received two points from its short bench as opposed to Dayton getting 34 from its reserves.