The high-flying flush came in the third quarter of the Pelicans' 117-115 triumph on Friday at the Smoothie King Center in New Orleans.
Pelicans guard Jrue Holiday dribbled through the paint on the play with about 9:14 remaining in the quarter. He dished back to a trailing Davis who was standing beyond the 3-point line. Davis faked a shot before dribbling into the paint.
He bounced the ball twice before lifting off and pulling the ball back in his right hand.
The 6-foot-11 Allen decided that he wanted to contest the shot, jumping straight up a few feet in front of the rim. But he shouldn't have.
Davis brought his right hand forward with authority, slamming the ball through the rim on a powerful finish.
"I saw him block Blake [Griffin] twice," Davis told reporters. "I figured I would try him and see what happens. He's a good shot blocker. But that's definitely going to be up there for this year."
Holiday later hit a game-winning jumper for the Pelicans with three 0:03 remaining. Davis had 18 points, 14 rebounds, five blocks, four steals and three assists in the victory. Holiday led the Pelicans with 26 points. D'Angelo Russell led the Nets with 24 points. Allen recorded seven points, nine rebounds, four assists, two blocks and two steals in the loss.