Washington was at his best during a second-half spurt, scoring eight straight points that helped the third-seeded Wildcats create a little breathing room in a back-and-forth game.
The freshman hit consecutive 3-pointers from the corner, just a few steps from Kentucky's bench, and then sank a floater in the lane that barely tickled the net and made it 69-60.
He added four free throws in the final 19 seconds to seal the victory inside a packed, pro-Kentucky crowd at Amalie Arena. Washington made 8 of 17 shots, including 4 of 5 from behind the arc.
Oscar Tshiebwe, a national player of the year candidate, notched his 14th consecutive double-double and 26th of the season with 12 points and 14
rebounds. That matches the single-season mark set by Kentucky great Dan Issel in 1969-70.
Kentucky won for the 15th time in its last 18 games and moved a step closer to securing a No. 1 seed in the upcoming NCAA Tournament. A win Saturday should do it: The Cats advanced to play No. 2 seed Tennessee in the second of two semifinals. Texas A&M and Arkansas will meet in the other.
Tshiebwe also had a career-high five blocks, and the Wildcats needed every one of them and then some to hold off the pesky Commodores (17-16) for the third time in two months.
Kentucky looked like it was going to pull away in the second half when it used a 15-1 run to turn a seven-point deficit into a seven-point lead. But Vandy coach Jerry Stackhouse called timeout to regroup, and the Commodores clawed their way back. Jordan Wright led Vandy with 27 points and Scottie Pippen Jr. cooled off with just 10.
Kentucky: Faces No. 2 seed Tennessee in a semifinal Saturday around 3:30 p.m. The teams split their regular-season meetings, with each winning at home.