The Rainbow Warriors (8-3) will play Mississippi State Saturday in the fifth-place game while the Utes (7-5) will meet San Diego for seventh.
Johnson shot 6 of 10 from the field, including 4 of 5 on 3-pointers. Thompson, who came off the bench after missing Wednesday's loss to Florida State due to a back injury, played 34 minutes and was 9 of 11 on free throws.
Josh Watkins had 16 points and Will Clyburn 14 for Utah, which was held to just 33.3 percent from the field and 1 of 15 from beyond the arc. David Foster added nine rebounds and four blocks for the Utes.