Thompson's play helped the Broncos (6-4) overcome a late 66-62 deficit and remain perfect in five home games this season. Boise State won despite shooting just 33 percent in the second half.
''It was amazing, that's all I can say about it,'' Thompson said. ''My teammates knew that I had the ball and that I was going to make a play. They knew that I was going to either make a play for myself, or for my teammates.''
James Webb III scored 17 points and pulled down 10 rebounds to lead Boise State, which made only 2 of 14 shots from 3-point range in the second half after making seven treys in the first.
Brandon Brown led Loyola Marymount (5-4) with 19 points. His potential winning 3-point shot with less than 1 second left was slightly off the mark.
''I am really proud of our guys tonight because there are a lot of teams that are down by four with 55 seconds left and would have hung their heads and thought it was over,'' Boise State coach Leon Rice said. ''But these guys found a way and got it done.''
The game featured 12 ties and 12 lead changes and was close throughout.
Boise State took its largest lead of the game at 20-14 on a Jackson 3-pointer with 11:20 left in the first half, but the Broncos scored only one point in the next 6 minutes to allow the Lions to take a 26-21 lead. Boise State led 37-36 at halftime.
In the second half, Boise State started ice cold from the field. The Broncos missed nine of their first 10 shots - including seven 3-pointers - and trailed 49-42 with 14:21 to play.
An 8-0 run gave Boise State back the lead. The Lions responded and took a 59-55 lead on a bucket by Cooper, who made 8 of 17 shots from the field.
Webb scored the game's next seven points to give the Broncos a 62-59 advantage. The Lions answered behind five points from Steven Haney, who finished with 16 points, to set up the finish.
''We've got to learn how to win on the road,'' Loyola Marymount coach Mike Dunlap said. ''It's a painful process, but a lot of good things came from this game.''
Loyola Marymount forward Adom Jacko recorded his second double-double of the season. He fouled out with 3:36 to play and finished with 12 points and 14 rebounds.
Loyola Marymount had a 39-32 edge on the boards. It was only the second time this season that the Lions outrebounded a Division I opponent.
Boston College transfer Lonnie Jackson made his first start at Boise State and responded with his third consecutive double-digit scoring game.
Boise State shot 29 free throws, compared to just seven for the Lions. ''Free throw disparity continues to be an issue for us,'' Dunlap said.
It was the first home game of the season in which Boise State did not score at least 100 points.
Boise State hosts Oregon on Saturday.
Loyola Marymount visits Cal State Fullerton on Saturday.