PHOENIX -- Arizona considers itself a good free-throw-shooting team, and it provided ample evidence Tuesday night.

The Wildcats made 20 free throws, 19 in the second half, and exploited No. 7 Texas A&M's foul trouble for a 67-64 victory over the Aggies in a battle of heavyweights in the Valley of the Sun Shootout at the Talking Stick Resort Arena.

"These guys will tell you, that is one of our team's strengths," Arizona coach Sean Miller said. "Twenty of 24 from the line, that's pretty much how we do it."

The Aggies made 7 of 10 foul shots.

Arizona freshman forward Deandre Ayton had 13 points and 10 rebounds for his fifth double-double. Brandon Randolph had 13 points, including four free throws in the final 27.4 seconds as the Wildcats maintained a slim lead.

Guard Parker Jackson-Cartwright gave Arizona a 61-58 edge on a 3-pointer with 1:54 remaining after Dusan Ristic tied the game with a basket on the previous possession.

The Wildcats (6-3) won their third straight after falling from No. 2 in the AP poll to out of the rankings completely following three straight losses in the Battle 4 Atlantis tournament two weeks ago.

"We're thrilled to win this game," Miller said. "I thought this was our best defensive effort of the year. This is something that you want to do to prepare your team for bigger things down the road."

Forward Tyler Davis had 21 points and guard Duane Wilson had 14 for the Aggies (7-1), who were attempting to start 8-0 for the first time in 10 seasons.

Randolph made two free throws for a 63-60 lead, and then made one each around a Davis field goal for a 65-62 edge with 5.8 seconds remaining.

The Aggies had one last chance when Wilson was fouled on a three-point attempt with 1.7 seconds remaining.

Wilson, who had made 18 of 19 free throws coming in, missed the first free throw but made the final two to cut the deficit to 65-64. He was trying to miss the last one, coach Billy Kennedy said.

After Arizona's Dylan Smith made two free throws, A&M missed a 40-foot 3-point try at the buzzer.

Ristic and Smith had 13 points apiece for Arizona, Smith reaching a season high.

Arizona made only eight field goals in the second half but converted 19 of 22 free throws, reaching the bonus with more than 10 minutes remaining.

"We put them on the line way too many times," said Kennedy, whose team shot seven free throws until the final second.

"You can't give good teams that type of advantage. The biggest thing is, we weren't ready to come out defensively like we should have at the beginning of the second half. I thought we lost the game at the beginning of the second half, not the end."

There were nine lead changes in the second half, six in the final 7 1/2 minutes.

The Aggies shot 45.6 percent from the floor and held a 30-29 rebounding edge. The Wildcats shot 42.9 percent from the field.

Guard Allonzo Trier, seventh in NCAA Division 1 with a 23.9 scoring average, scored seven points for the Wildcats, all in the second half. His first field goal, a 3-pointer with 17:07 left, gave Arizona a 36-33 lead.

Forward DJ Hogg, the Aggies' leading scorer at about 15 points a game, had nine points and five rebounds.

NOTES: Arizona 7-foot-1 freshman F Deandre Ayton, the reigning Pac-12 player of the week, is one of four players in NCAA Division I to average 20 points and 10 rebounds per game while shooting at least 60 percent from the field. He was averaging 20.4 points, 11.4 rebounds and shooting 61.4 percent before Tuesday. ... The Aggies beat Pac-12 contender and then-No. 10 USC 75-69 on Nov. 26. ... Arizona beat Texas A&M in Houston last season, weathering a late 18-0 run for a 67-63 victory.