Vinny Miller chipped in with 68 yards on nine carries and an 8-yard scoring run, which put The Citadel (4-2, 3-0 Southern Conference) in front, 14-7, for good.
The Citadel defense forced four three-and-outs and four turnovers.
Just 19 seconds after Smith's second touchdown, Mark Thomas had a strip-sack of Michael Eubank, which DeVonta Delaney returned 25 yards to give The Citadel a 35-14 lead with 37 seconds left in the second quarter.
On the first drive of the second half, Delaney picked off a Eubanks pass and seven play later, Smith scored his third touchdown and Samford (3-3, 1-2) trailed by at least three scores the rest of the way.
Karel Hamilton had 15 receptions for 220 yards - both career highs - and a score for Samford.