Mississippi State was 1-for-12 from beyond the arc in the half, while Alabama was 0-for-7, staying in the game thanks to 14 free throws.
For the contest, MSU hit 24 of 52 shots from the field (46.2 percent), 2 of 19 shots from 3-point range (10.5 percent) and 17 of 28 shots from the foul line (60.7 percent).
"I haven't coached many teams that didn't have an assist by halftime", Johnson said.
Now on its longest conference win streak since 2008, the Bulldogs moved to fourth place in the standings by snapping a four-game losing streak against Alabama, which fell to 15-9 and 6-5. The game marked Alabama's first rematch of the season as the Crimson Tide beat the Bulldogs 68-62 last month in Tuscaloosa, Ala.
Alabama dropped to 15-9 on the year, including 7-5 in SEC play.
Tennessee is led by sophomore forward Grant Williams who is averaging 16.2 points and 6.2 rebounds per game.
"I just have to do a better job of communitcating the message", Johnson said. "We just weren't very good offensively".
Petty's lone 3 came at a timely moment, giving the Tide a 54-53 lead, it's final advantage of the game, with 5:05 remaining.
MSU (18-6, 6-5) clearly got just enough offense to win and nearly all of it came from the Weatherspoon brothers.
The score was tied five times in the early going, including at 12 before Sexton broke the tie with a jumper and Alabama went on to take an 18-13 lead midway through the first half.
The Crimson Tide missed their next four straight field goals and made just 1 of its next 8 field goal tries, including missing 6 3s in a row.
STARKVILLE, Miss. (AP) - Nick Weatherspoon had 18 points and his brother Quinndary Weatherspoon scored 13 to lead Mississippi State past Alabama 67-63 on Tuesday at Humphrey Coliseum. "So we kind of sagged off 12 (Dazon Ingram) and 10 (Herbert Jones), all those guys to make them make shots".
"We knew that they didn't have a lot of shooters on the floor, that Petty was their main shooter", Weatherspoon said.
"We showed a lot of belief in one another. They made us want to defend and were great tonight".
Mississippi State's winning streak is adapting - and growing.
Alabama pulled ahead 49-45 in the second half when Sexton delivered an alley-oop opportunity that junior center Donta Hall slammed home to cap a 10-1 run.
Following the game against Tennessee, Alabama will host LSU on February 13 before heading on the road for back-to-back games against ranked opponents.
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