Rebels' coach Andy Kennedy was impressed. He also needs those numbers to become a habit.
"I want him to demand the ball even more," Kennedy said.
The 6-foot-9 Saiz scored 13 points in the first half to help the Rebels push out to a 46-35 lead. Stefan Moody added 22 points and shot 15 of 17 on free throws.
Ole Miss (2-0) won despite shooting just 36.4 percent (20 of 55) from the field.
Georgia Southern (1-1) trailed for nearly the entire game but pulled within 59-56 on Jake Allsmiller's back-to-back 3-pointers with less than eight minutes left.
The Eagles struggled to score the rest of the way and the Rebels pulled away for the win. The Eagles were led by Ike Smith's 14 points. Mike Hughes and Devonte Boykins both added 13.
Kennedy was frustrated that the Rebels struggled to put the Eagles away after leading by double-digits early in the second half.
"I know we practice," Kennedy said. "I've got the video evidence in case you want to see it. But I just wish we had better carryover and our attention to detail was better."
The game was filled with fouls and free throws. Ole Miss took advantage, making 40 of 53 (75.5 percent) from the free-throw line to keep the Eagles at arm's length for most of the night.
"We didn't adjust very well to all the fouls called," Georgia Southern coach Mark Byington said. "Really the game was won on the free-throw line by them. Give them credit — they've got some guys who can go off the bounce and put pressure on you."
Saiz had a breakout game after being a dependable role player for the Rebels over the past two seasons. He averaged 7.6 points and 5.5 rebounds last year as a sophomore and at 240 pounds has enough size to defend in the post.
But this is the first time Saiz — who is one of three starters returning from last season — has been asked to be a major of the offense. The Rebels feel good about Moody's ability to score after he averaged 16.6 points per game last season, but need a second option.
So far, Saiz has responded.
He scored 16 points and 14 rebounds in the opener last week and followed that up with another impressive performance on Monday.
Saiz scored on several low post moves and finished 8 of 14 from the field. He was also active on the offensive glass, grabbing four offensive rebounds and keeping several other balls alive for teammates to grab.
Saiz said it was nice to see his hard work in the offseason paying off during games.
"I worked on everything," Saiz said. "Going to the basket, dribbling and shooting."
Georgia Southern: The Eagles have 12 scholarship players and 11 of them are freshmen, redshirt freshmen or sophomores.
Ole Miss: Moody, who stands just 5-foot-10, had eight rebounds for the Rebels. Sam Finley added 12 points. Ole Miss shot just 2 of 14 (14.3 percent) from 3-point range.
Ole Miss vs. George Mason at the Gildan Charleston Classic on Thursday.
Georgia Southern at Auburn on Friday.