It's the second trip to the round of 16 in as many seasons under Calipari.
West Virginia, which reached the Final Four a year ago by beating Kentucky in the regional final, led 41-33 after closing the opening half on a 22-7 run. But Kentucky scored the first 11 points coming out of the break and eventually wore down the Mountaineers (22-12).
Josh Harrellson delivered eight of his 15 points during the pivotal stretch of the second half that Kentucky used to gain control. Terrence Jones overcame a slow start offensively to finish with 12 points and 10 rebounds, and each one of Knight's four assists produced easy baskets for teammates.
"He was really good," West Virginia coach Bob Huggins said of Knight.
"I thought we did a much better job the second half, but there's a reason why everybody recruits those guys; they're pretty good," Huggins added. "Terrence Jones made some huge plays for them, some huge baskets. They're talented ... really really talented."
Joe Mazzulla led West Virginia with 20 points, but the 6-foot-3 senior guard only had five after halftime. Darryl Bryant scored 15 before fouling out in the final minute, and Casey Mitchell came off the bench to add 11 and help the Mountaineers stay in the game.
For Calipari, it was just his second victory in 10 matchups with close friend Huggins. The two embraced after the final horn.
"I just wished him good luck," Huggins said. "I told him go win the thing."
Mazzulla was one of the keys to West Virginia's win last year, scoring 17 points and helping the Mountaineers frustrate Kentucky's shooters with a 1-3-1 zone that harassed the Wildcats into 4 for 32 from beyond the 3-point line.
West Virginia relied almost exclusively on man-to-man defense Saturday. And even though Kentucky shot 56.5 percent in the opening half, the Wildcats turned the ball over seven times and didn't get a lot of open looks at the baskets after getting off to its quick start.
Although the game was billed as a rematch of last year's East regional final, it really didn't feel like one.
Da'Sean Butler was the big gun on West Virginia's Final Four team and Kentucky is rebuilding after having five players — four freshmen — selected in the first round of the 2010 NBA draft, including No. 1 overall pick John Wall.
Knight missed his first seven shots before delivering the winner in Kentucky's 59-57 victory over Princeton on Thursday. He drained a pair of long 3-pointer to begin Saturday's game and never backed off.
"I felt more confident," said Knight, who was 9 of 20 from the field and made 9 of 10 free throws. "My teammates continued to have faith in me even though I didn't play such a great game (against Princeton). They still had faith in me, and they really helped me out, finding me and stuff like that. And they really stepped their level of play up, which got me more shots."
Knight scored 14 of his team's first 21 points, and Kentucky was in relatively good shape at the half despite not getting much production from it's other two freshmen starters — Jones and Doron Lamb — or junior Darius Miller. Lamb sat most of the opening half with three fouls and remained on the bench to start the second half, when the Wildcats used the 6-foot-6 DeAndre Liggins to try to slow down Mazulla.
The plan worked.
Kentucky opened the second half with an 11-0 run, taking the lead when Harrellson rebounded an airball and scored to bring Kentucky fans to their feet. Knight hit a layup and a 3-pointer during the surge, while also opening things up inside for the 6-foot-10 Harrellson, who left the game with a little over two minutes to left with a cut near one of his eyes that required four stitches.