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.
Gonzaga center Przemek Karnowski, who missed most of last season with a back injury, says he is returning for another year.
Wisconsin forward Nigel Hayes has withdrawn from the NBA draft and will return to the Badgers for his senior season.
Recruiting reporter Jeff Borzello has gotten grilled for his selections of underachieving and overachieving college basketball programs. He joins Phil Murphy to explain his rankings.