The Rebels (7-1) used a 12-5 run over the final 4:14 to seal it. The lead switched three times in the last 1:36, but Summers' three-point play with 34 seconds remaining put Mississippi ahead for good.
Down 35-34 at the break, Penn State began the second half on a 14-5 run.
The Rebels, who entered the game shooting 20 percent from 3-point range, were 11 of 24 (45.8 percent) from beyond the arc.
Penn State committed 15 turnovers but outrebounded Mississippi 34-30.
The Rebels had the size advantage, with all but one player on their roster standing taller than 6-foot-4.
"I just thought (Penn State was) tenacious," Mississippi coach Andy Kennedy said. "That was strictly effort and being tenacious and throwing bodies."
But down the stretch, it was all about the Rebels.
Mississippi outrebounded Penn State 7-2 in the final 4:14.
"We need to learn how to win those games," Penn State coach Pat Chambers said. "That was the first time we've been in one -- a dogfight."
Only one of the Nittany Lions' first eight games was decided by less than eight points.
Sunday's game was a coming-out party, of sorts, for Summers, a 6-foot-4 freshman making his fourth consecutive start. His 27 points were 13 more than his previous career-high.
Another highlight for the Rebels was their 3-point shooting.
"Trust me, it's an aberration," Kennedy said. "For the most part I thought they were clean looks, and for a change we knocked them down."