The Golden State Warriors All-Star was 7 of 10 from the field and 6 of 9 behind the arc, continuing to move a dismal start to the tournament for one of the game's best shooters.
Warriors teammate Klay Thompson added 15 points for the Americans, who advance to a game Tuesday against either Slovenia or Dominican Republic, who they are a combined 3-0 against this summer. The U.S. beat both easily in exhibition play, then handled the Dominicans again during the group stage in Bilbao.
Curry was just 4 for 17 overall in his first two games, though shot the ball over the next three. He saved his best performance for Barcelona, where the Americans are used to them.
He made consecutive 3s early in the third quarter when the Americans put away the game, the second coming as he was knocked down by a defender who was lucky not to be called for a foul.
Gustavo Ayon scored 25 points for Mexico, which won last year's FIBA Americas tournament to qualify and then advanced as the No. 4 team out of Group D despite a 2-3 record.
The six-foot-nine Ayon played for the Atlanta Hawks last season but had his season cut short by right shoulder surgery in February. He is a free agent and showed enough footwork and shooting touch to warrant a look from someone else.
But he couldn't prevent what ended up as the usual American romp in Barcelona, where the Dream Team crushed the competition in the 1992 Olympics.
The Americans averaged 117.3 points and won by 43.8 points a game then at nearby Badalona, but expect things to be a little more difficult here at the Palau Sant Jordi.
The U.S. surged to a quick 13-2 lead, and after Mexico answered with seven straight, pushed the lead back up to 23-13 after one. It stayed in double digits for nearly entire second, though Ayon had a 10-point period to keep the Americans from getting too far ahead, and it was 42-27 at halftime.
Curry's consecutive threes made it 50-27, and had back-to-back baskets again later in the third — including a layup for his only one inside the arc — before DeMarcus Cousins' bucket made it 57-30.
Despite being bordering countries, the teams hadn't met since the 2007 Olympic qualifying tournament. They hadn't played in the World Cup since 1967.
James Harden finished with 12 points for the U.S.
Follow Brian Mahoney on Twitter: http://www.twitter.com/Briancmahoney