Borchert had a game-high 22 points and was 7-of-12 from the field, including 2-of-4 beyond the arc. Meanwhile, Ware had 21 points and a career-best 16 rebounds for the Bulldogs (10-3).
Ware had 12 points and 11 rebounds in the first half for his fifth double-double of the season. MSU ended the half on a 13-6 run and held a 29-20 lead.
"It gave me a confidence boost," said Ware. "It's been tough when teams double me but tonight we had a good size advantage and my guys fed me the ball."
The Bulldogs shot 46.8 percent for the game and knocked down 6-of-15 3-pointers. The Hawks (2-10) shot 41.3 percent and had just four free throws the entire game. MSU was called for just seven fouls in the game and made 13-of-18 free throws.
Mississippi State held a 43-29 advantage on the boards, including 18 offensive rebounds. Along with Ware's career night, Roquez Johnson had nine rebounds and his nine points.
The Bulldogs' 10th win matched the win total of head coach Rick Ray's first season in Starkville.
"It was a good milestone to reach already," said Ray. "When you get to 10 wins after having all of 10 wins last season. But now we have to see what we do from here on out and now we get to go against SEC foes."
Maryland-Eastern Shore made just 1-of-13 beyond the arc in the first half but made seven three-pointers in the second half and got within nine points with 3:19 left in the game. But that would be the closest the Hawks would get the rest of the way.
"We didn't do a good job and biggest concern I had coming off the Christmas break was us having a flavor for the competition," said Ray. "I didn't think we had that and we didn't finish around the rim. But it was good to get back and get the win."
Both teams struggled offensively in the first half. Mississippi State shot just 39 percent in the opening half while the Hawks were worse than that at 29 percent in the opening 20 minutes.
Mississippi State's Craig Sword was held to just three points and just three shots from the field. It snapped an 11-game streak of double-digit scoring games for the Bulldog sophomore.