The miscue occurred about three minutes before the end of the second quarter during the 110-109 setback on Thursday at Oracle Arena in Oakland.
Warriors star Stephen Curry began the sequence by using a screen from Green to clear a path toward the rim. Curry dribbled past the 3-point line and stop right before reaching the paint. He then fired a pass back to Green on his left.
Green and Thompson ran toward each other as Green appeared to be setting another screen. The Warriors forward picked up the ball in his right hand and tossed it directly at Thompson's face, drilling the sharpshooter in the forehead.
The ball bounced over half court and eventually went out of bounds. Golden State had 15 turnovers and made just 6-of-15 free throw attempts in the loss.
"It was a wild game. It was a strange game," Warriors coach Steve Kerr told reporters. "I didn't think we competed very well in the first half. I loved the way we competed in the second half and if we play with that type of intensity and competitiveness for the whole game, then we are in business. But we gotta put it together for 48 minutes."
Green and Thompson each scored 15 points for the Warriors. Curry netted a game-high 29 points while Kevin Durant scored 26 points in the loss. Jusuf Nurkic had 27 points for the Trail Blazers. C.J. McCollum and Damian Lillard scored 24 points and 21 points, respectively.
The Warriors get a rematch against the Trail Blazers at 10 p.m. on Saturday at Moda Center in Portland.