The Huskers then took the lead three times in the extra period.
Adds details.Tony Carr scored nine of his 17 points, including a game-winning long jumper with three seconds left in overtime, and Penn State beat Nebraska 76-74.
Carr, who was 2 of 17 from the field in regulation, hit 3 of 4 shots in overtime.
Watson knocked down a pair of free throws with 5:32 left for his first points of the second half to cut PSU's lead to seven, and Copeland followed that up with 3-pointer to pull within 61-56 with just over four minutes to play. At game's end, forward Isaiah Roby tried a 45-footer that was short.
"You can't just get blasted in the first half like that", Nebraska coach Tim Miles said. "I called a timeout and I said, 'Guys, one of two things is going to happen: one, we're going to get embarrassed, or two, we're going to decide to just play harder than these guys".
"For as many good things as we did, we did just enough to lose".
The execution of the final attempt in regulation drew criticism from Miles.
The Cornhuskers (12-7, 3-3 Big Ten) struggled to contain Penn State's team-high scorers Lamar Stevens and Mike Watkins - each tallied more than 20 points. Watson missed a 3-pointer on the Huskers' final possession, and the game went to overtime tied 65-65.
The Nittany Lions kept their foot on the pedal coming back for the second half - progressing that late surge to a 13-0 run.
Miles said he couldn't offer an update yet on Tshimanga's status.
Penn State hosts Minnesota (13-5, 2-3) on Monday.
Glynn Watson carried the load to open the game, scoring Nebraska's first seven points and making four of his first five shots from the field.
Penn State quickly reclaimed the lead on four straight points by Carr, but with 14 seconds on the clock, Anton Gill knocked down a clutch 3-pointer to tie it up at 74-74.
Five points off the bench from freshman Thomas Allen helped NU pull back to within 26-24 with just under three minutes to go in the half, but the Nittany Lions would close out on a 7-0 run from there to go into halftime up 33-24.
But NU forward Isaac Copeland sparked a comeback. Stevens, who has finished in double figures in each of the last nine games, led the charge with almost half of his team's points during that first period of play, tallying 16 off 5-9 shooting.
Nebraska led 15-12, but the Nittany Lions went on an 8-1 spurt, keyed by five points from Lamar Stevens, to build a 20-16 lead with 8:15 left in the first half.
"Tony had the guts to come out and hit some big shots for us when he didn't have the best shooting night", Chambers said.
In his absence, head coach Pat Chambers needed to find increased depth - giving usual sixth-man Jamari Wheeler his first start as well as putting forwards Trent Buttrick and Deividas Zemgulis on the floor for their first Big Ten minutes of the season.
NU's leading scorer, guard James Palmer, had his worst night as a Husker.
Then, after missing his previous nine shots, Watson drained a 3-pointer from the top of the key to make it a two-point game.
The Cornhuskers return home to host IL on Monday and MI on Thursday.