The Billikens (6-6) trailed for most of the first half and went into the intermission down 38-30. They opened the second half with an 18-3 run and never trailed again.
The Camels (5-6) used an 8-1 run to close within 60-56 on Chris Clemons' free throws with 3:34 left, but Goodwin stopped the momentum with a 3-point play and Saint Louis made 9 of 12 free throws to go with Davell Roby's layup to hold on to the lead.
Johnson made all three of his 3-point attempts, all six of his free throws and 4 of 6 overall from the field for Saint Louis. Hasahn French added 11 points and 12 rebounds.
Chris Clemons had 28 points and Marcus Burk had 20, accounting for all but 18 of the Camels' points.
Mannion, who recently reclassified and is ESPN's No.11 overall player in the class of 2019, chose Arizona over Marquette.
He'll fit in with Sean Miller's plans for a faster tempo on offense.
The cream of the crop of American high school basketball will congregate in Colorado Springs from Oct. 5-7, as USA Basketball unveils its newly expanded Junior National Team minicamp in collaboration with the NBA, NCAA and NBPA.