Rebecca Murray poured in 22 points for the defending Paralympic champions and they used strong defence to pile on the punishment for winless Mexico, converting 20 turnovers into 19 points.
'I feel we could play better but this was a good win for us coming off that Germany loss,' said Murray. 'Sometimes in losing you learn a lot more than when you win, so it was good to put things right today.'
Desi Miller added 18 points for the USA, who made it two wins out of three in Group B, while Estrada Bernal scored 10 for Mexico, eight of them in the first half.
Germany and China will join the USA in the next round after the Germans made it two wins out of two, defeating France 76-32 behind 23 points from Marina Mohnen.
Gesche Schuenemann added 15 and Annika Zeyen 12 for Germany, while captain Angelique Quemener-Pichon had 12 for France. China were not in action but hold the tie-breaker over Mexico.
In Group A, hosts Great Britain got off the mark with a 42-37 win over Brazil.
Bouncing back from yesterday's 51-24 loss to Australia, Britain used an 8-0 fourth quarter run to turn a 35-31 deficit into a 39-35 lead, turning a tight contest in their favour.
Amy Conroy scored 18 points for Britain.
In the men's draw, Dirk Koehler scored 16 points to lead Germany into the quarter-finals as they made it three wins out of three in Group B with a 64-49 win over Japan.
The USA are on the verge of securing their last-eight place after routing South Africa 91-29 in Group A.
Matt Scott had all 21 of his points in the first half, many of them during a 25-0 second-quarter run that ended the game as a contest. Joshua Turek also added 19 points.
Turkey's Gem Gezinci and Ali Asker Turan celebrated their birthdays with a 65-60 win over Italy.