Mississippi State (13-5, 3-2 Southeastern Conference) led by 10 points midway through the second half before Auburn rallied and Chris Denson's layup cut it to 59-58 with 4:35 remaining.
But little-used Mississippi State reserve Tyson Cunningham scored the next five points -- and then took a charge on the other end -- to help the Bulldogs hold on for the victory.
Johnson made 4 of 7 shots from the field, but did most of his work on free throws, hitting 10 of 16.
Mississippi State has beaten Auburn 13 out of the last 14 times at Humphrey Coliseum.
It's been an agonizing three weeks of basketball for Auburn, which has lost all five of its SEC games. All of them have been competitive.
The Tigers jumped out to an 8-0 lead and led for most of the first half before things fell apart. Mississippi State went on a 20-4 run to turn a 21-14 deficit into a 34-25 advantage by halftime. Craig Sword's steal and dunk with just three seconds left in the half finalized the impressive rally.
Borchert had 11 first-half points, including three 3-pointers, which were critical in helping the Bulldogs pull out of the early hole.
Borchert and Johnson helped Mississippi State shrug off a tough offensive night for Sword and Gavin Ware, the team's top two scorers.
Sword shot just 1-of-6 from the field and scored six points while Ware was limited to just four minutes in the first half because of foul trouble. Ware's back-to-back buckets midway through the second half helped the Bulldogs push out to a 51-41 lead.
Auburn had one run remaining. The Tigers scored the next eight points, using a full-court press defense that forced Mississippi State into some bad decisions and turnovers. Denson's layup cut the lead to 59-58 and things looked good for the Tigers.
But then it was Cunningham's time. The 6-foot-3 senior is averaging just 1.5 points per game, but made two free throws and then nailed a 3-pointer from the corner to push the lead back to 64-58.
Then he stood his ground when Auburn's Harrell slashed toward the basket, drawing the charge. Auburn never threatened again.
Harrell finished 9 of 17 from the field, including 4 of 8 from 3-point range.
Mississippi State's bench outscored Auburn's 28-0.
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Maryland point guard Melo Trimble, considered a lock to leave the program before struggling in the second half last season, has withdrawn from the NBA draft and will return for his junior season.
Louisville's Chinanu Onuaku, who recently underwent a medical procedure to correct a heart rhythm issue detected during the combine, will keep his name in the NBA draft pool.
Andrew White III will return to the Nebraska men's basketball team next season after removing his name from the NBA draft.