Butler got downhill and hit a 17-foot two-point shot as time expired completing a remarkable 14-point second-half comeback for the Aztecs.
It was the first buzzer-beater during this NCAA tournament and only the fifth in the Final Four history.
Aztecs coach Brian Dutcher opted against calling a timeout when Nathan Mensah rebounded Johnell Davis' missed jumper with the Owls leading 71-70 with 10 seconds left, before Butler drove on and took responsibility with his buzzer-beater for the ages.
"I didn't really know how big it was," Butler said who was mobbed by teammates and coaches. "We're going to the national championship. That's not things many people do."
After trailing 40-33 at half-time, SDSU found its defensive grip to work its way back into the contest, with Matt Bradley scoring 21 points with six rebounds.
Alijah Martin top scored for FAU with 26 points including three triples along with seven rebounds.
The Aztecs will face UConn who accounted for the Miami Hurricanes 72-59 with forward Adama Sanogo outstanding with 21 points including two three-pointers and 10 rebounds.
UConn advanced to their fifth National Championship game, with the Huskies having not lost to a non-conference opponent this year and winning all five NCAA games by double digits.
Huskies guard Jordan Hawkins overcame illness to contribute 13 points, while Miami's Isaiah Wong scored a team-high 15 points on four-of-10 shooting with their offense blunted, going at 32.3 per cent from the field as a team.
Timme, a senior, was named a consensus First-Team All-American this year after back-to-back Second-Team selections in his sophomore and junior seasons.
While his career at Gonzaga has been littered with individual honours, the six-foot-10 fringe NBA prospect looked destined to end his run as a Bulldog without capturing their elusive first National Championship as they trailed 46-33 at half-time.
But Timme would not let three-seed Gonzaga go down quietly, putting together a monstrous 36 points on 16-of-24 shooting while adding 13 rebounds, four assists and two blocks to turn their deficit into a 72-62 lead with 2:30 remaining.
UCLA's Jaime Jaquez Jr made things interesting with a quick eight-point burst on his way to a team-high 29 (12-of-25 shooting), 11 rebounds, three assists and three steals, setting up Amari Bailey for a three-pointer to put the Bruins back in front 76-75 with 13 seconds on the clock.
With the game on the line, Julian Strawther drained the clutch three to give Gonzaga the lead and the win, booking their fifth Elite 8 trip from the past eight editions of the tournament.
Gonzaga will face the four-seed Connecticut Huskies next after they wiped the floor with the eight-seed Arkansas Razorbacks 88-65.
It was another strong performance from UConn's top NBA prospect Jordan Hawkins, as the lanky six-foot-five wing dropped a game-high 24 points on six-of-13 shooting with three assists, marking the third tournament game in a row he has drained at least three three-pointers.
The nine-seed Florida Atlantic Owls are through to their first Elite 8 in school history after upsetting the four-seed Tennessee Volunteers 62-55.
The Owls came into the tournament at 31-3, and while there were questions about their strength of schedule, they have continued to prove they are one of college basketball's best teams this year, holding Tennessee to just 33 per cent shooting.
Florida Atlantic will play Kansas State in the next stage after the Wildcats survived a thrilling 98-93 overtime battle against Tom Izzo's Michigan State Spartans.
Five-foot-eight Wildcats point guard Markquis Nowell played the game of his life, ending up with 20 points (seven-of-18 shooting), 19 assists, five steals and just two turnovers in his 43 minutes.
He joins Chris Paul and James Harden as the only players from either division one college basketball or the NBA in the past decade to put up a game of at least 20 points, 15 assists and five steals.
It is not just the first Final Four the Owls have ever reached, as they had never won a game in the NCAA Tournament prior to this season, with their only previous appearance being a first-round exit in 2002.
After knocking out eight-seed Memphis, 16-seed Fairleigh Dickinson and four-seed Tennessee, Florida Atlantic won the East region and cut down the nets by eliminating the third-seed Wildcats.
The Owls had to deal with another spectacular performance from Kansas State talisman Markquis Nowell as the five-foot-eight point guard put up 30 points (eight-of-21 shooting), 12 assists and five steals.
But while the Wildcats leaned on their star, Florida Atlantic spread it around, with four players scoring at least 13 points, led by Bryan Greenlee's 16 on four-of-seven shooting. Seven-foot-one Russian center Vladislav Goldin controlled the interior with 14 points (six-of-11), 13 rebounds and two blocks.
The win means Florida Atlantic will play the winner between Creighton and San Diego State for a spot in the National Championship game.
It was far smoother sailing on the other side of the bracket as the four-seed Connecticut Huskies pummelled the three-seed Gonzaga Bulldogs 82-54 in a statement-making effort.
UConn's top draft prospect Jordan Hawkins drained six triples for his 20 points and six rebounds, while do-it-all wing Andre Jackson Jr flirted with a triple-double, finishing with 10 assists, nine rebounds and eight points.
It is the first time in NCAA Tournament history a team seeded fourth or lower won four consecutive games by double digits.
With it, Connecticut earned their sixth Final Four trip in program history, and first since 2014. They will meet the winner between five-seed Miami and two-seed Texas for a spot in the final game of the season.
The Spartans rode a 23-point performance from senior point guard Tyson Walker, while Joey Hauser – brother of Boston Celtics wing Sam Hauser – collected 14 points and 10 rebounds.
As well as pulling into a tie for the sixth-most Sweet 16 appearances in head coaching history, Izzo also claimed the record for the most ever NCAA Tournament wins as the lower seed, with this his 16th.
He is one more Sweet 16 trip away from tying Louisville legend Denny Crum for the fifth-most, with only North Carolina's Roy Williams (19), Syracuse's Jim Boeheim (20), Michael Jordan's North Carolina coach Dean Smith (21) and Duke's Mike Krzyzewski (26) having more.
The seven-seed Spartans will next face three-seed Kansas State after they won the battle of the Wildcats 75-69 against six-seed Kentucky.
Reigning National Player of the Year Oscar Tshiebwe was monstrous with 25 points and 18 rebounds, while projected first-round draft pick Cason Wallace impressed with 21 points (nine-of-11 shooting), nine rebounds, four assists and two steals.
But their performances were not enough to lift Kentucky to the victory, as diminutive five-foot-eight point guard Markquis Nowell dropped a game-high 27 points and nine assists to carry Kansas State through.
Following his massive 28-point, 13-rebound showing in his side's opening-round win, Connecticut Huskies center Adama Sonogo starred again with 24 points (11-of-16 shooting) and eight rebounds in a 70-55 win over the Saint Mary's Gaels.
After Marquette, the top seed to fall Sunday was the three-seed Baylor Bears. Despite 30 points from Baylor guard L.J. Cryer, the Creighton Bluejays received a game-winning 30 points from Ryan Nembhard in the 85-76 triumph.
Nembhard is the younger brother of Andrew, who has been a rookie standout for the Indiana Pacers this season.
Following their stunning upset of one-seed Purdue, where they became the second 16-seed to ever advance past the first round, the Fairleigh Dickinson Knights were sent packing 78-70 by the nine-seed Florida Atlantic Owls.
Three-seed Xavier were in control throughout their 84-73 win against Pittsburgh, five-seed Miami prevailed 85-69 over four-seed Indiana, and four-seed Gonzaga sent six-seed TCU home 84-81.
