The Aggies and Tigers were tied 1-1 after two overtime periods, but A&M (15-6-3) won 4-2 in penalty kicks to advance to the third round of the tournament. Top-ranked Florida State will host A&M next weekend, with the the time and date to be determined later.
Aggie freshman Mary Grace Schmidt connected on the first PK, then Dyer stopped SEC offensive player of the year Malorie Rutledge. A&M's Rachel Shipley, Cydne Currie and Peterson each made their kicks before LSU's Melissa Clarke hit the crossbar to end the match.
"Kelly Dyer is one of the best goalkeepers I've ever been around as far as penalty kick situations," A&M coach G. Guerrieri said. "We knew that if we put our balls in the back of the net that Kelly would take care of the rest."
The Aggies applied pressure throughout the first half but couldn't come up with a goal. They finally struck in the 66th minute when Peterson headed the ball inside the far post off a corner kick by Shipley.
Two minutes later, Rutledge was fouled in the penalty box and Clarke scored on the subsequent penalty kick to even the match.
In the first overtime period, the Aggies had two good opportunities. The best came in the 95th minute, when Nora Skelton slid a pass to Katie Hamilton at the top of the box and her shot from 16 yards was scooped up at the near post.
In the second overtime, Currie fired off a shot from outside the box that went just over the crossbar. LSU countered, and a dangerous cross to Clarke in the box slipped through everyone and went over the end line.
A&M had an 18-10 shot advantage and held LSU without a shot on goal for the final 29 minutes of the match.