Meshke carded 70-70-75--215 for a six-stroke individual victory, while Iowa State completed a wire-to-wire win with 297-304-304--905.
Texas A&M finished second at 916, with two individuals in the top four -- Christa Spedding with 78-71-72--221 and Brenda Norris with 74-73-75--222.
Arkansas, ranked 19th, lost its two-year grip on the title and finished third at 303-310-307--920, one shot ahead of No. 7 Missouri.
Iowa State had three players in the top nine, as Louise Kenney tied Spedding for second at 73-76-72--221 and Christi Athas tied for ninth at 228.
Katie Brophy shot a 3-under-par 69 for the best round of the tournament to help Notre Dame jump into fifth place at 922.
Jill Marcum of Iowa aced the tough 17th hole in a round of 76 for the 12th-place Hawkeyes.
Courtney Mahon had Arkansas' best closing round with a 39-36--75, after slipping to an 82 on Monday.
Amanda McCurdy, despite a painful kidney stone, led the Lady Razorbacks for the tournament with 73-77-78--228, tying Athas for ninth place.
McCurdy took some pain medication Tuesday after throwing up until the wee hours of the morning.
"We had to carry her to the car after Monday's round," said David McCurdy, Amanda's dad.
At least on Tuesday, McCurdy played the final three holes in even-par, with a bogey from a bunker at No. 17 and a successful 15-foot birdie putt at No. 18.
She'll have one more chance, next year.
Kelley Hester, Arkansas' third-year coach, said, "It's kind of ironic that we won this the last two years and then didn't win it this year with our most talented team. We haven't come close to firing on all cylinders yet."
Arkansas freshman Stacy Lewis tied for 12th with 78-74-77--229.
Gena Johnson, a UA senior from Hot Springs, struggled to a 43-36--79 on Tuesday but was honored by the Arkansas Women's Golf Association afterwards as its Player of the Year.
Mahon credited her improved play on Tuesday with better focus. "Every shot was important for the team, so I just tried to grind it out," she said. "We had a good fall overall and proved ourselves as one of the top teams in the country."
In attendance was former UA golfer Craig Lile, who tied for second at Odessa, Texas, on the Nationwide Tour last week and jumped to 42nd on that tour's money list.
"I'm relaxing today," Lile said. "Mondays and Tuesdays are my weekend."
Meshke, Iowa State Cruise To Title
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