After John Lucas missed a 3-pointer for Baylor with about 5 seconds left, Kasib Powell grabbed the rebound and passed to Ross, who missed a contested layup.
"I was just going to run and hopefully be there to congratulate Ron when he laid it in," Ellis said. "I was going to chase it anyway, and it happened to come off right to me."
Ellis caught the ball in midair, his 10th rebound, and stuffed it in with nine-tenths of a second left as Tech (21-7, 10-6 Big 12) completed its first regular season under coach Bob Knight.
"I've never had a kid make a better play than that at the end of the game," said Knight, in his 35th season as a head coach. "I think most guys would have stood and watched.
"When Ross went in and didn't dunk the ball, I won't tell you what all I said. He had a clear-cut drive to the basket," Knight said. "It just amazed me that all of a sudden the ball's dunked on the follow."
The Raiders overcame a 10-point deficit in the final 13 minutes. They remained in contention for a first-round bye in next week's Big 12 tournament.
Tech ran off the court thinking the game was over. The Raiders were called back after officials reviewed television replays and determined that Baylor (14-15, 4-12), which has lost six straight games, had time for one more play.
The inbound pass by R.T. Guinn, who had contested Ross' shot and appeared to foul the shooter, was knocked down by Andre Emmett.
"That last play didn't lose the game," said Baylor coach Dave Bliss, an assistant for Knight at Army (1967-69) and Indiana (1971-75). "We lost it when we didn't pick up all of the loose balls and rebounds. It was a disappointing game."
Ellis' inside basket over Guinn with 2:52 left made it 86-85. That ended a 7-0 run that gave Tech its first lead since midway through the first half.
After Lawrence Roberts' putback off the glass, Ellis hit a 3-pointer with 1:43 left. Guinn's putback of Lucas' missed 3-pointer tied the game at 89 with 1:04 left.
Lucas then stole the ball from Ross, but his shot was blocked by Nick Valdez with 36 seconds left. Baylor kept the ball, and decided to hold for one shot, but Lucas was forced to take a long 3-pointer.
"I didn't have that much faith in our defense," Bliss said. "We had trouble on defense all day, so we ran our shot-clock play."
Tech shot 55 percent, hitting 35-of-64 shots. Baylor shot 49 percent (32-of-66), including 14-of-31 3-pointers.
Emmett had 27 points and 10 rebounds for the Raiders and Powell added 25 points. Three other players combined for Tech's other 11 points.
Guinn had 22 points, including four 3-pointers, and 13 rebounds and Roberts also scored 22 points to break the Big 12 freshman scoring record. Lucas had 19 points with five 3-pointers.
Roberts has 475 points this season, one more than Texas A&M's Bernard King scored as a freshman two years ago.
Baylor has led 69-59 when Lucas made a layup with 12:42 left. It was seven minutes more before Ellis made a 3-pointer, the first of the game by Tech, to cut the lead in half, 78-73.
The Red Raiders won't know until Sunday if they will finish in the top four of the Big 12 standings and get a first-round bye in the tournament. Going into the weekend, there were 41 different possible scenarios.
"We took care of our part. That's all we could do," Ellis said. "We'll see what happens after that."
Baylor led 46-42 at halftime, and 3-pointers were the difference. The Bears made 8-of-16 treys and Tech missed all nine of its long-range shots in the first half. Tech made all three of its 3-pointers after halftime.
The 14 3-pointers left Baylor one short of its school record 265 in a season.