Elliott scored a season-high 22 points to help the fifth-seeded Wildcats end Chattanooga's 26-game winning streak with a 69-59 victory Saturday.
Kentucky, back in the NCAA tournament for the first time since 1999, meets last year's runner-up Michigan State, a 65-46 winner over Wisconsin-Milwaukee, in the second round of the Bridgeport Regional on Monday.
Elliott reached the 20-point mark for the third time in four games and grabbed 11 rebounds for Kentucky. She scored 16 in the first half as the Wildcats grabbed an eight-point lead.
Samantha Mahoney added 14 points, and Jennifer Humphrey scored all of her 11 in the second half. She was 1-for-3 from the field, but 9-for-12 from the free-throw line for the Wildcats (22-8).
Alex Anderson scored 17 points for Chattanooga (27-4), which fell one win shy of the school record it set two years ago. That streak ended with a second-round loss to Vanderbilt in the NCAA tournament.
This time, the 12th-seeded Lady Mocs never found their touch from the outside.
Chattanooga, which set a Southern Conference record with 245 3-pointers and was second in the nation averaging 8.2 per game, shot just 6-of-27 from beyond the arc.
Chattanooga won 27 straight two years ago, beating Rutgers in the first round of the NCAA before losing to Vanderbilt. Kentucky routed the Lady Mocs 91-54 in the second round of last year's WNIT behind former Wildcat Sara Potts' seven 3-pointers and 32 points.
Although this one was closer, the Wildcats' lead never really seemed in jeopardy. With shots banging off the rim and backboard, Chattanooga never mounted a serious threat.
The Lady Mocs closed to 55-47 after a fastbreak layup by Tiffani Roberson. But a jumper, steal and layup by Mahoney bumped Kentucky's lead to 59-47 with just over 8 minutes left.
Chattanooga pulled to 63-56 on two free throws by Roberson with 3:20 remaining, but Elliott answered with two foul shots of her own.
Kentucky, making its sixth tournament appearance, led most of the first half and took a 39-31 lead into the locker room.
The 6-foot-6 Elliott, averaging 10.9 points, dominated inside, hitting 7-of-8 shots and grabbing five rebounds.
The Lady Mocs shot 4-for-11 from 3-point range in the first half, with Brooke Hand hitting 3-of-4, and things didn't get better.