Then, left fielder Evan Mistich ripped home two more on a two-out single.
But UConn got out of it when designated hitter Matt Oberste bounced a fielder's choice to the second baseman.
The Huskies seized a 3-0 lead in the top of the first when Sooner starter Steven Okert got off to a shaky start.
Reine, Oberste and shortstop Caleb Bushyhead each recorded RBIs to help tie it back up at three in the bottom of the third, as OU scored one in the second and two in the third.
But UConn added two more in the sixth and eighth and one in the ninth before OU's furious rally.
The loss drops OU to 9-4 on the year, and it returns to action at 1 p.m. CT/11 a.m. PT against future conference mate West Virginia before playing host Oregon, the No. 9 team in the nation, at 9 p.m. CT/7 p.m. PT.
"It will be an exciting day of baseball and hopefully the weather holds up," Golloway said. "I am thankful for the two games tomorrow because we have to get better."