The victory gave the Americans a measure of revenge against the tiny West African county that knocked them out of the previous two World Cups and put the U.S. and Germany on top of the Group G, with Ghana and Portugal at the bottom.
Dempsey's goal came on a low shot just 32 seconds into the match. Ghana dominated much the rest of the game, and Andre Ayew levelled in the 82nd minute.
Just four minutes later, Brooks — a 21-year-old who came on at halftime because Matt Besler was injured — headed in a corner from Graham Zusi. It was the first time an American sub had ever scored in the World Cup.
Dempsey's goal made him the first U.S. player to score in three different World Cups and was the fastest ever scored by an American in the tournament.
GERMANY 4, PORTUGAL 0
SALVADOR, Brazil (AP) — Thomas Mueller scored a hat trick as Germany turned on its style and power to rout 10-man Portugal 4-0 in their World Cup Group G opener on Monday.
Mueller, who scored five goals at the 2010 World Cup, was ruthless against a weak Portugal team that was clearly outplayed.
With Chancellor Angela Merkel supporting in the stands, the German team celebrated its 100th World Cup match with a rousing victory that virtually assured by halftime.
Mueller scored either side of Mats Hummels' headed goal as Germany took a 3-0 lead at the break, and added his third goal in the 81st.
Portugal was already 2-0 down before Pepe was red carded in the 37th minute for head-butting Mueller when the German player was sitting on the ground.
IRAN 0, NIGERIA 0
CURITIBA, Brazil (AP) — Nigeria and Iran delivered the first draw of the World Cup on Monday as they ground out a scrappy 0-0 stalemate in their opening match in Group F.
The draw at the Arena da Baixada in the southern Brazilian city of Curitiba followed 12 mostly high scoring and attacking games.
After a first half in which Nigeria failed to capitalize on its dominance, chances were few and far between in the second.
In the early passages of play, Nigeria had shown menace, with much of its attacking thrust coming down the left with Emmanuel Emenike and Victor Moses combining to cause problems for the defensively-minded Iran side.
Nigeria came closest to scoring in the seventh minute when an Ahmed Musa goal was disallowed after John Obi Mikel was adjudged to have fouled Iran goalkeeper Alireza Haghighi at a corner.