Jackson drove for a layup with 28 seconds left to give the Bears a 54-52 victory over Mississippi State (No. 14 ESPN/USA Today, No. 15 AP), which had won 11 straight.
"A lot of players wouldn't have the guts to take the last shot or make the last play," Baylor coach Scott Drew said. "He made a great move, got to the hole and finished it, and I think that shows his heart and his courage."
Especially after missing several earlier chances to either tie the game or put the Bears ahead. Jackson finished with a game-high 14 points, the last when he took advantage of a screen by Quincy Acy to drive around Dee Bost.
"Actually, my teammates just told me to move on to the next play," Jackson said. "And I got a good look and I laid it up."
The Bears (13-0) are off to their best start in school history, winning their first game against a ranked opponent this season on a night when No. 4 Louisville and Indiana (No. 15 ESPN/USA Today, No. 13 AP) had already lost for the first time. Baylor is one of four undefeated teams left in Division I.
Mississippi State (12-2) still had another chance after Jackson's drive. But Rodney Hood lost control of the ball going up for a shot when Acy knocked it away. Jackson then swatted the ball to the other end of the court, and Drew emphatically pumped his right arm as the game ended.
"The key to their team is Jackson. He's the guy that makes them go," Mississippi State coach Rick Stansbury said. "They've got a lot of other guys on that team that can score a lot of different ways, but Jackson's ability to manufacture baskets, that's the key."
The Bulldogs didn't score again after Acy was called for goaltending on a shot by Arnett Moultrie, making it 52-50 with 3:20 left.
But with just under 3 minutes left, Jackson missed the front end of a 1-and-1. He then had a steal but missed the breakaway layup.
"For people that don't know Pierre, he doesn't usually miss layups like that," Drew said.
Then Jackson missed a 3-pointer from the top of the key, but Acy got knocked to the ground and Renardo Sidney was called for his fifth foul with 1:35 left and then a technical for his reaction to the call.
Quincy Miller made one of the free throws for the technical before Acy made a free throw to tie the game at 52.
Bost missed a shot for Mississippi State, then almost forced a turnover on the other end without being able to keep the ball in bounds.
Then came Jackson's game-winning play.
"Quincy Acy sets great ball screens, so every time they play the screen instead of the person who has the ball, which is me, I refuse it," Jackson said. "And I had a wide open lane."
Jackson had scored eight consecutive points during regulation and overtime in their last game, an 83-81 victory over West Virginia on Friday night in the Las Vegas Classic championship game.
"The last two games they won, who won them? Jackson," Stansbury said. "The two close games they had, he jumps up and makes that 3 against West Virginia and he makes those penetration plays against us late. That's what makes them so tough, they got a lot of different weapons."
Miller had 12 points for Baylor and Brady Heslip had 11, all before halftime.
Jalen Steele and Sidney each had 10 points, while SEC rebounding leader Moultrie had eight points with 10 rebounds. Sidney was 5 of 6 from the field, but played only 19 minutes because of his foul problems.
The Bulldogs lost for the first time since a 68-58 setback to Akron in the second game of the season. Their winning streak included consecutive wins over Top 25 teams Texas A&M and Arizona.
Mississippi State had its biggest lead of the game when Bost had a steal that lead to a breakaway two-handed slam by Sidney for a 46-42 lead with 8:40 left.
About a minute later, Bost made a floater in the lane for a 50-48 lead, but that was the last ball the Bulldogs actually put through the hoop since Moultrie's basket was on a goaltending call.
Heslip had three 3-pointers in the first half.
The Bears led 24-19 when Heslip hit a 3-pointer with 6 minutes left in the first half, and had another 3½ minutes later that made it 34-28.
But Mississippi State scored the last five points of the half, cutting the deficit to 34-33 on a 3-pointer by Brian Bryant and a driving layup by Moultrie.
"The game is a fine line, it comes down to inches. Inches here or there," Stansbury said. "I know we left four free throws on that backboard in the last minute, I know that."