The Eagles (1-1), who are reclassifying from Division II to Division I, led for the entire second half until Pledger connected from the right wing with 15.2 seconds left to tie the game at 58.
North Carolina Central was trying to snap a 40-game losing streak on the road and nearly pulled it off against an Oklahoma team coming off a losing season and with nine newcomers on the roster.
Pledger finished with 14 points and Nick Thompson had 12 rebounds and seven assists for Oklahoma.
Wilkerson, Clement and Chasten hit consecutive 3-pointers to put North Carolina Central ahead midway through the first half, and the Eagles were able to stay ahead until the final minute of regulation.
Fitzgerald scored Oklahoma's first 10 points of the second half just to keep the Sooners in the game, and North Carolina Central led by as many as six after Fitzgerald went to the bench with his fourth foul.
Pledger rattled in a 3-pointer from the left corner to cut the deficit to 56-55 with 1:06 remaining and give the Sooners a chance. He then came through with the biggest shot after Wilkerson's two free throws stretched the lead back to three.
Calvin Newell had the ball knocked away by Emanuel Chapman but was able to recover it along the left sideline and throw a cross court pass to Pledger, who was open on the right wing for the tying shot.
Before then, the Sooners were in jeopardy of losing for just the third time in 81 nonconference games since 1999.