Sidney, who scored his season-high of 24 points against the Rebels in a win earlier this season, was 8 of 12 from the field and also grabbed 12 rebounds.
Mississippi State (14-12, 6-6 Southeastern Conference) has won five straight games in the series.
Ole Miss (17-10, 5-7) critically damaged what was left of its slim NCAA Tournament at-large hopes. The Rebels scored the final seven points of the first half to tie the score at 33, but Mississippi State went on a 13-2 run early in the second half and never trailed again.
Riley Benock hit two 3-pointers and Sidney threw down a thunderous dunk during the rally, whipping the announced crowd of 8,063 into a frenzy that seemed to rattle the Rebels.
For one of the few times this season, Sidney made news for great basketball instead of off-the-court issues. The 6-foot-10 sophomore has been suspended three times this season -- once by the NCAA after it ruled he received improper benefits as an amateur, once for an incident during practice and once for a fight with a teammate.
But those troubles didn't matter against the Rebels. Instead, he was the dominant force many projected him as coming out of high school, controlling the post and scoring several easy baskets.
Mississippi State shot 50 percent in the second half to pull away, including 50 percent (5 of 10) from 3-point range.
MSU and Ole Miss came into the game in a three-way tie with Arkansas for second place in the SEC's Western Division. The first two teams in each division get a first-round bye in the SEC Tournament.
Ole Miss outrebounded MSU, 41-34.