Postell scored a 9.9 on the beam to finish behind Georgia's Grace Taylor (9.95) and Baskett scored a 9.8438 to finish second on the vault behind LSU's Susan Jackson (9.8563).
Postell also scored a 9.9 on the floor to finish fourth as the last competitor of the night, in her last collegiate routine.
"I'm excited," Postell said of her post-gymnastics future. "I'll miss it, but I had fun this weekend."
Postell said she had no regrets about her routines. Beam she thought she could have done a little better, and she wasn't bothered by a slight step on floor, knowing she couldn't beat Georgia's Courtney McCool who earlier scored a 9.9625.
"I knew I couldn't get three tens, I'm not that special," she said.
Baskett's night had highs and lows Saturday.
She stuck both her vaults and finished with a 9.8438 as the first competitor on the vault. That score managed to hold up even with 10 competitors behind her. Auburn's Julie Dwyer posted the same score and the event was won by LSU's Susan Jackson (9.8563).
"First up, I was really happy it held up," she said.
Baskett placed sixth on the uneven bars and was one of the favorites for the floor title, but couldn't finish her routine after her takeoff on her first pass was too low and she landed short, spraining her left ankle.
"I'm glad it happened on the last event," she said. "It sucks, but at least I have a long time to recover."
Baskett, who was the bars co-champion in 2006 and finished fourth in 2007, wasn't as crisp as she has been in her routine and scored a 9.875 to finish sixth.
Postell had a great uneven bars routine going until she landed and took a big step forward and received a 9.8. Postell finished 16th out of the 18 competitors. UCLA's Tasha Schwikert, who won the all-around title Thursday, won the bars with a 9.9375.
Postell leaves with one NCAA title, a balance beam championship she won in Salt Lake City last season.
"I didn't have any goals during the week, I didn't want to put that pressure on myself," she said. "I just wanted to hit my routines."
The performance she had was typical of the consistently strong routines she has delivered throughout her career.
"We're going to miss her," Utah coach Greg Marsden said. "You obviously don't replace her."
Kyndal Robarts, Utah's surprise qualifier on the vault, sat her first vault and scored just 8.5375 for her combined vaults, finishing last. Robarts was deducted a point for performing the same vault twice. She was going to do a different vault for her second, but did the same after falling on the first.
VAULT: Kristina Baskett - 2nd, 9.8438; Kyndal Robarts - 10th, 8.5375
* UNEVEN BARS: Kristina Baskett - 6th, 9.875; Ashley Postell - 16th, 9.8
* BALANCE BEAM: Ashley Postell - 9.9, 2nd
* FLOOR: Ashley Postell - 9.9, 4th; Kristina Baskett - 2.55, 14th