Smith, the tournament's top seed, earned a 6-2, 6-3 victory over No. 16 Clay Donato of North Carolina in the afternoon's round of 16.
In the evening, Smith picked up his second win against a top-10 opponent this year, defeating No. 6 Dimitar Kutrovsky of Texas for the second time in his career. Smith breezed through the first set 6-1. He fell behind three games to start the next set, but rallied back to win 7-5. He defeated Kutrovsky in straight sets last season at the NCAA Championships.
"J.P. keeps on winning -- he never takes a match off," Tennessee associate head coach Chris Woodruff said.
Smith improved to 9-0 against ranked opponents and faces another one Saturday in the semifinals: No. 18 Steve Johnson of Southern California.
Conkic and Williams defeated Florida's Antoine Benneteau and Alexandre Lecroix 8-6 in the quarterfinals to improve their season record to 9-1. With the match tied 6-6, Conkic and Williams won the last two games to secure the match.
"Boris and Rhyne played great today," Woodruff said. "They just got stronger as the match went on."
Conkic and Williams match up in the semifinals against Bradley Klahn and Ryan Thatcher of Stanford, the eighth-ranked doubles team nationally and the tournament's third seed. Conkic and Williams are 1-1 against top-10 opponents this season.
With the win, Conkic extended his doubles winning streak to a team-leading 12 matches and has not lost since Sept. 27. The streak started with five victories he and Smith earned on their way to the title at the ITA All-American Championships last month.
Smith and senior Davey Sandgren, the tournament's top-seeded pair, lost their quarterfinal match 8-3 to Texas A&M's Jeff Dadamo and Austin Krajicek.
The Indoor Championships mark the final tournament stop for the Vols this fall, and Woodruff feels good about where the team chemistry is headed.
"I like where the unity is at right now," Woodruff said. "Sam and I have noticed that whenever we've traveled with the team this fall. Hopefully that's something that will carry on into the spring season."
ITA National Intercollegiate Indoor Championships
New Haven, Conn.
Round of 16
(1) John-Patrick Smith, UT, def. Clay Donato, North Carolina, 6-2, 6-3
John-Patrick Smith, UT, def. (6) Dimitar Kutrovsky, Texas, 6-1, 7-5
Conkic/Williams, UT, def. Benneteau/Lecroix, Florida, 8-6
Dadamo/Krajicek, Texas A&M, def. (1) Sandgren/Smith, UT, 8-3