The Sooners finished just ahead of Alabama's score of 197.350 and behind Florida's winning score of 197.575.
The second-place finish ties for the highest in program history. OU also placed second in 2010.
"Before we went out we said no regrets, and in the end there wasn't one more toe we could point, there wasn't one more landing we could stick," said OU head coach K.J. Kindler. "We did everything in our power to do the best we could. They laid their hearts out there."
A huge 49.475 on beam, .250 better than the next best score on the event, put OU at 147.975, just .15 behind Alabama and .125 behind Florida going into the fourth and final event.
The Sooners got big beam routines from sophomore Rebecca Clark, who set a career high with a 9.925, and junior Madison Mooring, also with a 9.925.
Spears added a 9.9, Lauren Alexander scored 9.875 and Keeley Kmieciak and Erica Brewer each submitted a 9.85.
Oklahoma then went to floor and scored a 49.400 to close out the night, but Florida's 49.475 on bars sealed the Gators' win.
"The emotion was incredible," Kindler said. "After landing we had people crying and tearing up and absolutely losing their minds. You could see the passion was there and what better time than the night of the national championship."
Senior Brie Olson scored a 9.925 to lead OU on her final routine as a Sooner. Mooring added a 9.9.
The Sooners were in fourth place at the midway point in a close meet, with their 98.500 just .250 off from Alabama in the top spot with a 98.750.
Erica Brewer, Brie Olson and Haley Scaman all recorded 9.9s for OU, which totaled a 49.375 overall.
After one rotation, OU held second place with a 49.125 on vault, just behind UCLA at 49.375 and ahead of Georgia at 49.050 and Florida, forced to count a fall on beam, at 48.875.
Freshman Maile'ana Kanewa and Spears tied for the team high on vault with a pair of 9.85 scores.
The Sooners' score of 197.375 is the highest by an OU program at the NCAA Championships and gives OU its 13th meet with a score of 197 or above, tying an NCAA record for most such meets in a season with Florida in 2007.
Brewer, Clark and Mooring will close out the season for Oklahoma by competing in the Individual Finals on Sunday at 3 p.m. CT. Mooring will compete on vault, Brewer and Clark will compete on bars and Brewer will compete on beam. The competition will be shown live on ESPN3.com.