Ellis was 3 of 7 from the field -- all 3 makes coming from 3-point range -- and knocked down a game-high six free throws.
Army (3-1) took a 31-30 lead into halftime after Kyle Wilson made a layup as time expired in the first half.
The Black Knights opened the second half with eight unanswered points to go ahead 39-30. St. Francis cut the deficit to 45-44 with 10:06 left but Army held the Terriers to just one point over the next six minutes to pull away.
Army outshot St. Francis (1-2) 42.9 percent (24 of 56) to 33.9 percent (20 of 59) and got 35 points off the bench compared to just 10 for the Terriers.
Jalen Cannon led St. Francis with 23 points and 10 rebounds.
Mike Krzyzewski says he has good reason to be excited for next season thanks to a combination of Duke's incoming freshmen and a core of experienced upperclassmen.
Georgia guard Juwan Parker has been awarded a medical redshirt, leaving him with two years of eligibility, after missing the 2015-16 season with a partially torn Achilles tendon.
Forward Trevon Bluiett has withdrawn from consideration from the NBA draft and will return to Xavier for his junior season.