Connecticut (27-6) advanced to its first regional final since winning the national championship in 1999. The Huskies will meet No. 1 seed Maryland with the winner going to the Final Four.
Freshman Ben Gordon's three-pointer gave the Huskies the lead for good at 16-14 with 12 minutes left in the first half and triggered a 13-4 spurt. Butler hit a three-pointer and Tony Robertson added a jumper with just under seven minutes left to cap the run for a 26-18 advantage.
Gordon's three-pointer with 35 seconds left capped an 8-2 spurt as Connecticut went to halftime with a 40-28 cushion.
"We kind of grabbed control late in the first half," Huskies coach Jim Calhoun said. "That 12-point cushion was something to build on."
The Huskies maintained the advantage in the second half and had a 53-41 lead on freshman Emeka Okafor's dunk with 10:35 remaining. Butler had a dunk for a 60-49 lead with 5 1/2 minutes left.
Southern Illinois (28-8) pulled within 62-56 when Jermaine Dearman made one of two free throws with three minutes remaining.
Butler responded with a basket and two foul shots for a 66-56 advantage with 1:51 left.
"We couldn't sleep on this team," Butler said. "They had good quality wins throughout the season. They're a dangerous team."
Connecticut made five of nine shots from beyond the arc in the first half while the Salukis missed all six attempts. Southern Illinois finished at just 1-of-14 for the game and star guard Kent Williams was none of five.
"I knew we had to stop Williams," Huskies point guard Taliek Brown said. "We played good defense on the guards."
"He never got in a rhythm," Southern Illinois coach Bruce Weber said. "I thought Kent had open looks. It's a kid you want to do well because of his dedication to the work ethic. He needed to get one down early but he never did."
Butler made just six of 16 shots but was the catalyst on the defensive end as the Salukis shot just 38 percent.
Williams and freshman Darren Brooks each finished with seven points, combining to miss 14 of 19 shots.
Butler came off a 34-point effort against North Carolina State in the second round. The 22-year-old sophomore has often talked about the success of former Connecticut stars like Ray Allen and Donyell Marshall and how he wants his name mentioned with those players in time.
"I want to put the team on my back and lead them to a Final Four, a national championship," Butler said. "Coach Calhoun has given me the opportunity to do that."
Gordon netted 12 points off the bench and Robertson chipped in 10 for the Huskies, who survived despite making only nine baskets in the second half. Connecticut also was just 18 of 30 from the free-throw line.
Rolan Roberts led the Salukis with 24 points. He was limited to just eight points in the second half as Okafor and Huskies reserve forward Mike Hayes clamped down on defense.
Dearman added 17 points for Southern Illinois, which made its deepest tournament run and closed the season with a school-record 28 victories. But Williams' struggles prevented the Salukis from doing further damage.
"We attacked with Jermaine and Rolan right from the start," Weber said. "I thought we'd be able to go inside-outside and get good perimeter shots."
Dearman grabbed nine rebounds and Roberts added eight as Southern Illinois held a 40-38 edge on the glass. The Salukis took advantage of 18 offensive rebounds for a 21-14 edge in second-chance points.