Kentucky (25-10) advances to the second round of the South Region, where it will meet 13th-seeded Buffalo. The Bulls stunned fourth-seeded Arizona 89-68 on Thursday.
An eight-time NCAA champion making its record 58th tourney appearance, Kentucky won for the 25th time in its past 26 first-round tournament contests and improved to 46-10 all time in NCAA openers.
"These guys have never -- they're all freshman -- they've never been in this tournament, and they think Davidson is going away," Kentucky coach John Calipari told CBS after the game. "This is life and death and hopefully a good lesson for us going forward."
Shai Gilgeous-Alexander added 19 points, eight rebounds and seven assists and PJ Washington scored 11 for Kentucky, which won the Southeastern Conference championship against Tennessee on Sunday.
"We're just fighting on both ends of the basketball court, playing more together on the offensive end and getting everybody shots, and on the defensive end we're locking in," said Knox, whose team has won eight of its past nine games.
Jon Axel Gudmundsson drained six 3-pointers and scored 21 points to lead Atlantic 10 champion Davidson (21-12), which was making its 14th tourney appearance and its ninth under coach Bob McKillop.
Davidson's leading scorer, Peyton Aldridge, was held to 12 points on 4-of-17 shooting, Kellan Grady added 16 points and Will Magarity had 11. It was the 10th anniversary of the Stephen Curry-led Davidson team's run to the Elite Eight.
Kentucky was up 34-24 at halftime and led by as many as 13 before Gudmundsson got hot from long distance in the second half, knocking down his first five 3-pointers of the half to pull Davidson into a 52-all tie with 9:04 remaining.
It went back and forth until Knox's two free throws with 2:50 made it 63-59 and sparked a 9-0 run to put Kentucky up by 10 points with just under a minute to play.
Davidson didn't go away quietly in the final minute, but was unable to come closer than five as KiShawn Pritchett's 3-point attempt with two seconds left brought the game to its final score.
It was the second-ever meeting between Davidson and Kentucky in the NCAA Tournament. Kentucky earned a 75-55 win in the opening round of the 1986 tourney.
--Field Level Media
Davidson | Kentucky | |
Jon Axel Gudmundsson 21 | Scoring | Kevin Knox 25 |
Jon Axel Gudmundsson 3 | Assists | Shai Gilgeous-Alexander 7 |
Will Magarity 6 | Rebounds | Shai Gilgeous-Alexander 8 |
Kellan Grady 7 | Free Throws Made | Shai Gilgeous-Alexander 9 |
Kellan Grady 1 | Steals | Shai Gilgeous-Alexander 5 |
Peyton Aldridge 1 | Blocks | Hamidou Diallo 3 |