BOISE, Idaho -- With his fifth-ranked team trailing by two points in the final seconds, San Diego State coach Steve Fisher was all but certain senior point guard Xavier Thames was going to take the final shot for the Aztecs on Wednesday night.

But Thames surprised his coach -- and most of the 9,602 in attendance -- when he whipped a pass to Dwayne Polee II, who drained a 3-pointer with 4 seconds left to give the Aztecs an improbable come-from-behind 67-65 victory that extended their winning streak to 19 games.

"It was like the Red Sea parted," Polee said. "I wasn't surprised. X is a real unselfish player, and if there was one person open, he was going to find them."

Thames finished with 23 points for San Diego State (20-1, 9-0 Mountain West), but it was his steal at midcourt in the final minute and his second assist of the game that saved the Aztecs, who trailed by 14 points in the second half.

"What can you say about Xavier Thames?" Fisher asked. "You can't tell me that he's not playing as well as anyone in America right now."

Thames said he was very close to taking a shot that would have tied the score. But at the very last second, he changed his mind.

"I had a pretty decent look, but I saw DP out of the corner of my eye," Thames said. "I was going to shoot a floater but (Ryan) Watkins was going to contest it. Then I saw (Anthony) Drmic sink down. It was on the tip of my fingers (to shoot). It was pretty close."

Close is the typical result when the Aztecs and Broncos (15-8, 5-5) play. The past six meetings between the schools have been decided by six or fewer points. San Diego State eliminated Boise State from the past two conference tournaments and won 69-66 last month in San Diego.

"They're a good matchup for us, and we're a good matchup for them," Thames said. "We know we're always going to get a great game for them."

Mikey Thompson led the Broncos with 16 points and Thomas Bropleh and Derrick Marks both added 15.

"I just feel awful for these guys right now," Boise State coach Leon Rice said. "They are giving everything they have. We just haven't finished."

Boise State led the final 18 minutes of the first half and the first 15 of the second before a scoring drought allowed the Aztecs to rally. After Bropleh banked in a 3-pointer to give the Broncos a 57-43 lead with 13:37 to play, Boise State only made one field goal in the next 11 minutes and the lead disappeared when Thames scored his seventh consecutive point to give his team a 61-59 lead with 4 minutes to play.

Boise State finally got on track, getting two free throws and a layup from Thompson and a basket from Marks to retake the lead at 65-62. Thames made a steal in the final minute and hit two free throws after being fouled, and after Marks missed a jumper, the Aztecs were in position for the biggest play of the game.

"That was a tough, gutty character-type game for us," Fisher said. "We stayed with it and found a way to win."

Thames said there was some motivation to keep the winning streak going. With its meteoric rise to No. 5 in the poll, the Aztecs expect to get every team's best shot the rest of the way.

"We talked at halftime about that," he said. "We said, `You know they are going to rush the court if they win.' We didn't want that to happen."

Josh Davis had 10 points for San Diego State, which won despite turning the ball over 15 times and allowing Boise State to shoot 51 percent from the field and make eight 3-pointer.

"They just kept hitting shot after shot," said Polee, who finished with nine points and was 1 for 1 on 3-point attempts. "Everything they threw up was going in. We just had to buckle up."

The win was the 10th straight win away from home for San Diego State and its ninth straight conference win.