Mississippi State (8-20, 3-13 Southeastern Conference) ended nearly two months of misery with the victory. The Bulldogs led almost the entire game, pushing back every Ole Miss rally in the second half.
Roquez Johnson returned from a three-game suspension to score 10 points for Mississippi State.
Ole Miss (21-8, 10-6) lost for the sixth time in 10 games. Murphy Holloway led the Rebels with 22 points and 19 rebounds. The SEC's leading scorer Marshall Henderson had 16 points, but shot just 4 of 19 from the field, including 3 of 18 from 3-point range.
The Rebels shot just 25 of 74 (33.8 percent) from the field.
Ole Miss jumped out to an early 5-0 lead, but then it was Mississippi State that was the aggressor.
Borchert hit 3 of 4 3-point attempts on the way to 11 first-half points, helping the Bulldogs build a 34-30 halftime lead.
The 6-foot-8 junior was terrific for most of the night, finishing from long range and close to the rim. After he hit the early 3-pointers, Ole Miss played him tight, but then he would drive to the rim and convert.
Mississippi State pushed its lead to 45-36 with 15 minutes left after Borchert's nifty reverse layup in traffic, but then the Rebels methodically started a comeback, pulling within 45-43 on a Jarvis Summers basket with 10:53 remaining.
That's when Reginald Buckner made arguably Ole Miss' biggest mistake, earning a technical after being called for a foul. That earned the 6-foot-9 senior his fourth personal foul and a spot on the bench just when it looked like the Rebels might be gaining some momentum.
Mississippi State went nearly seven minutes without a field goal midway through the second half before Borchert hit a jumper from 15 feet and Trivante Bloodman made a 3 to give the Bulldogs a 52-45 advantage with 7:30 remaining.
The loss might be the fatal blow to Ole Miss' hopes for an NCAA tournament at-large bid. The Rebels have a home game against Alabama and a road game at LSU remaining.
Ole Miss had a 17-2 record and was the 16th-ranked team in the nation just a month ago, but has now dropped six out of the past 10. Those losses include setbacks against South Carolina and Mississippi State, two of the bottom three teams in the league.
Against the Bulldogs, the Rebels were a mess of poor decisions and bad shooting.
Henderson, who has galvanized Ole Miss all season with his long-range shooting, couldn't hit from 3-point range even though he had several wide-open looks. Holloway was the only consistent performer for the Rebels, dominating on the glass for his 36th career double-double, but it wasn't enough.
Follow David Brandt on Twitter: www.twitter.com/davidbrandtAP