The loss snapped a two-game winning streak for the Commodores (13-9, 4-5), who had won 27 of their previous 30 at home over the last two seasons.
Hayes had a team-high 13 rebounds, and Rajon Rondo added 12 points for Kentucky, which is off to its best start since the 1998 NCAA title team began the season 19-2.
Kentucky took control from the beginning by scoring the first nine points. Vanderbilt missed its first four shots and didn't get on the board until Przybyszewski's 3-pointer five minutes into the game.
By then, it was too late.
The Wildcats led 46-29 at halftime after Azubuike hit a 3-pointer at the buzzer. They led by as many as 71-47 midway through the second half. Vandy managed to get within 10 twice in the final minute, but it was too late.
The Commodores outrebounded Kentucky 37-33 and shot the ball about as well as the Wildcats (25-of-51 compared to 31-of-63). But they were only 8-of-26 from 3-point range, and Kentucky turned its 19 turnovers into 30 points.
Vanderbilt hit five of its first six shots in the second half and used a 9-2 spurt to pull to 54-42 on a free throw by Jason Holwerda with 16:21 left. But Sparks helped Kentucky put the game out of reach.
Sparks first hit a 3-pointer. Smith answered with a 3, then Sparks scored on a layup. Hayes made a 3-pointer, then Sparks followed up with his own 3 and a layup. He stole the ball, and Ravi Moss scored on a layup that capped a 17-5 run for the 71-47 lead.