Glory Johnson added 18 points for the second-seeded Lady Vols (27-8), who'll meet the winner of Georgia Tech-Baylor on Monday night for a spot in the Final Four.
"The first half we tend to get ourselves in a hole, but we fought back," said Tennessee associate head coach Holly Warlick. "I thought our bench was outstanding."
The Lady Vols trailed 26-12 in the first half, but cut the deficit to 35-30 by halftime. They took the lead for good with a 19-9 run to open the second half.
Angel Goodrich had a game-high 23 points and Aishah Sutherland had 19 for Kansas (21-13), which fell to 0-3 in regional semifinals.
Simmons helped pick up the sluggish Lady Vols.
"She has a scoring mentality. We've said she's never seen a shot she didn't like. But I tell you what, a lot of those shots she takes she makes," Warlick said. "If we can learn from her and understand that great things can happen when you have a lot of heart, we won't get down like that in the first half."
Tennessee couldn't do anything right for the first 11 minutes, falling behind to a Kansas team that finished below .500 in the Big 12.
But there's a reason the Lady Vols always seem to be in the regional finals. The Jayhawks found out in the opening minutes of the second half, when Tennessee's superior depth and athleticism simply overwhelmed the underdogs.
"The second-chance points on the glass, the offensive rebounds, which is what they've always been about," Kansas coach Bonnie Henrickson said. "They got into us in the offensive glass, they got into us in transition. That's the way they got the separation in the second half."
The Lady Vols finally took the lead, 44-42, thanks largely to back-to-back 3s from Ariel Massengale, and a pair of free throws made it 53-46 Tennessee with 11:07 to go.
Freshman post player Chelsea Gardner did her best to keep the Jayhawks close with 14 points and 10 rebounds. But Simmons hit a layup off a give-and-go from Baugh to give the Lady Vols their first double-digit lead, 63-53, with 7:07 left.
Shekinna Stricklen had 16 points and nine rebounds for Tennessee, which shot 51. 5 percent in the second half.
This looked like the ultimate mismatch at the outset. Kansas was playing in just its third regional semifinal, while Tennessee was playing in its 30th and shooting for a record 19th Final Four.
But early on, the Jayhawks seemed ready for the late morning start.
Gardner bullied her way for four inside buckets in the opening five minutes, and back-to-back layups through the paint by Goodrich gave Kansas a surprising 18-10 lead. The Lady Vols called timeout in an effort to quell the run, but Goodrich and Tania Jackson buried 3s to help push the lead to 14 points.
"The first couple of minutes we came out with a lot of energy on defense and offense. We were hitting a lot of shots," Gardner said. "We just had great defense."
That's the kind of deficit that will get anyone's attention. They Lady Vols came out of a timeout with considerably more energy, responding with an energetic 19-5 run to get back within 31-29.
Kansas lost star Carolyn Davis to a knee injury last month, but rallied to earn its first regional semifinals berth since 1998 with upsets of Nebraska and third-seeded Delaware.
Tennessee's seniors now have the opportunity to avoid becoming the first four-year class in school history to miss the Final Four. They got it in large part because of the work of Simmons.
"Since it's a one and done kind of thing, it just brings that energy inside me. Seems like I have that alter ego," Simmons said. "I want to go out there and prove a point that I'm better than what people thought of me. I want our seniors to go to the Final Four."