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Que Morrison added 16 points for the Bulldogs (21-9) and also collected eight rebounds, while Jillian Hollingshead scored 15 points.
Makira Cook led the Flyers (26-6) with 21 points.
The first half featured six lead changes and four ties, before Georgia seized control.
Morrison scored to give the Bulldogs a 25-20 advantage. Hollingshead followed with a jumper and layup that pushed the margin to 29-22.
A 3-pointer by Morrison extended Georgia’s lead to 38-26 with 2:31 left in the second quarter.
Dayton continued to struggle with the Bulldogs’ size as Hollingshead and Staiti, both 6-foot-4, continually found defensive mismatches.
The duo connected on back-to-back baskets to give Georgia a 54-41 lead with 2:07 left in the third quarter.
Dayton shot 36% percent from the floor.
Georgia is making its 35th NCAA Tournament appearance in the event’s 40-year history, tying the Bulldogs with Stanford for second on the all-time list. Tennessee is tops with 40 NCAA appearances. Georgia was seeking its 58th win in the tournament.
Dayton struggled to match its torrid shooting from two nights earlier. The Flyers made 13 of 23 shots from 3-point range in an 88-57 First Four win over DePaul on Wednesday. Against Georgia, they made just two of their first seven attempts from behind the arc. Dayton finished 6 of 18 from long range.
Georgia improved to 10-4 away from home this season. This was the first-ever meeting between Dayton and the Bulldogs.
Georgia advances to meet the winner of Friday’s matchup between Iowa State and Texas-Arlington in a second-round game on Sunday.