The Hawks were down 56-51 with 8:30 to play, but surged back to tie the game, 56-56, on a 3-pointer by Ware.
The Hawks never trailed again, and the win was capped by a Ware dunk for the last Hawks basket of the night with 11 seconds remaining.
“I am proud of our guys’ ability to make winning plays down the stretch,” said coach Chad Warner.
“In order for us to have a chance next Saturday (home against No. 9 Alabama-Huntsville) we will have to be much better. Union played very well and physical. We were fortunate to get the win.”
Walter Hill finished with 13 points for Shorter.
Kenny Leverette and Hill pulled in seven rebounds apiece, just behind the nine that Banks totaled for the game.
The Hawks went 16-for-19 from the free throw line, with Banks going 6-for-6.
Shorter turned 14 Union turnovers into 23 points, while outscoring the Bulldogs 34-28 in the paint.
Shorter will have a week to prepare for Alabama-Huntsville, which will come to the Winthrop-King Centre on Saturday.
In other action Saturday:
SHORTER WOMEN 64,
Karisma Boykin finished with 19 points, including the game-winning 3-pointer in the final seconds, as the Lady Hawks withstood a late Union rally and earned a GSC win at home.
Three other Lady Hawk starters reached double digits in points.
Former Coosa star Ieshia Alexander had 12 points, former Model star Shelby Farrer added 11, and Lynette Harris had 10.
Harris registered a game-high nine rebounds.
Union came into the game with the top record in the GSC and winners of three straight games, but the Lady Hawks (9-6, 5-3 GSC) snapped the surge.
The Lady Hawks saw an 11-point second half lead disappear over a five-minute span to find themselves down by one with less than 10 minutes remaining.
The teams traded baskets and free throws from there, with the Lady Hawks holding a 61-58 advantage with 1:23 remaining.
Amy Philamlee hit a 3-pointer and made an easy lay-up to put Union (10-5, 5-2 GSC) on top inside of the final minute.
Boykin then missed a 3-pointer but the shot but Kristin Nash grabbed the rebound and passed to Boykin for the game-winner.
“It was a great win today against a very good Union team” said coach Vic Mitchell.
“We showed a lot of heart with the way we battled … (I’m) really proud of our team and now they will get a couple of well-deserved days off before getting back to practice on Tuesday.”
The Lady Hawks will host Albany State on Thursday.
GHC TEAMS SWEPT BY CENTRAL GEORGIA TECH
Shakierya McClendon, Seandre Lee, Gabrielle Kendal and Shan’Taja Latimore each scored 14 points for GHC, but it wasn’t enough to overcome a bad night at the free thow line in a 71-69 loss to Central Georgia Tech.
GHC, which finished 16-for-29 at the foul line, fell to 16-4 on the year and 9-3 in conference play.
The Lady Chargers return home on Wednesday to face Atlanta Metro College.
In men’s action, GHC’s Dimychael Ross had 20 points and JR Davis had 13 but the Chargers fell to Central Georgia Tech, 65-61.
The Chargers return home on Wednesday for a conference game against Atlanta Metro College.
The Berry College men placed first and the women were second at the Viking Classic, which concluded Saturday at the Cage Aquatic Center.
Berry’s men closed the meet with a pool record swim in the 400 freestyle relay. The quartet of Graydon McCrite, Johnathan Purdy, Cameron Grant and Conor Monaghan posted a 3:16.15.
“This was truly a great job from both the men and women,” said Berry head coach Paul Flinchbaugh.
“Records fell and I’m overjoyed with the performances. With one home meet left, the men are undefeated at home. Looking back at our Winter training trip in Puerto Rico, we are now seeing the benefit of all our hard work and effort.”