Taylor, a preseason All-Southeastern Conference selection, shot 7 of 9 from the field. Johnson, a freshman, came off the bench and made 9 of 10 free throws.
Thirteen players scored for the Commodores, who made 63.2 percent of their shots. Vanderbilt also made 10 3-pointers in the first half.
John Jenkins, the SEC's top scorer last year (19.5 ppg), led the way with three 3-pointers. He finished with 15 points and freshman reserve Shelby Moats added 10.
Anthony Simmons and Wanto Joseph each scored 11 points for Xavier.
Vanderbilt was without 6-foot-11 starting center Festus Ezeli. He will miss at least six weeks after spraining ligaments in his knee two weeks ago during practice.
The Commodores, with their highest preseason ranking since the 1960s, begin their season at home Friday against Oregon.
Vanderbilt 102, Xavier (La.) 62
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