Carlos Vela produced a scintillating individual goal, weaving through the San Jose defence, dribbling the goalkeeper and nonchalantly scoring from close range.
New York Red Bulls midfielder Adams burst into the penalty area to tuck away an Antonee Robinson cross.
Brazil superstar Neymar brushed off his critics after firing the five-time World Cup winners to victory over Mexico on Monday and enter into a quarter-final showdown with Belgium.
Brazil overcame a tricky start to the last-16 tie, as second-half goals from Neymar and Roberto Firmino sealed a deserved victory.
Neymar scored the first goal in the 51st minute. Roberto Firmino then scored in the 88th minute to seal the win for Brazil.
FIFA World Cup 2018, Highlights, Brazil vs Mexico: Neymar and Roberto Firmino scored in the 51st and 88th minute respectively to help Brazil qualify for the quarter-finals of the World Cup.
A Brazil side finding their stride in Russia after a slow start are arguably the toughest challenge Mexico could have asked for as they were punished for failing to back up victories over Germany and South Korea with defeat to Sweden to finish second in Group F.
For a seventh straight World Cup, Mexico have made it to the last 16, but, agonisingly, they have failed to go any further on the six previous occasions.
Mexico and five-time World Cup champions Brazil are set to clash in their Round 16 match on Monday.
Suggestions on Twitter that the FIFA World Cup be restricted to 10 ten teams were greeted with laughter.
"Korea! Korea!" chanted fans in a Mexico City bar, leaping into the air and embracing when the Asian side scored a stoppage-time, VAR-assisted goal, and then a late second to seal the reigning champions' humiliating exitand allow Mexico to squeak through to the Round of 16.
Sweden surged into the last 16 of the World Cup with a deserved 3-0 victory over a poor Mexico side, who still qualified ahead of Germany after the holders' loss to South Korea.
FIFA World Cup 2018, Highlights: Sweden finished top of Group F after beating Mexico 3-0 at the Ekaterinburg Arena.
The 30-year-old striker's goal in the 2-1 victory over South Korea on Saturday made him the first Mexican player to score 50 goals for his country (in 104 appearances).
Mexico would be keen to top the FIFA World Cup 2018 Group F, while Sweden need a good result.
Sweden need a good result vs Mexico in the 2018 FIFA Woerld Cup Group F.
Mexico lead Group F on six points after two games.
FIFA World Cup 2018, Highlights Korea Republic vs Mexico: Mexico beat Korea Republic 2-01 to record their second successive win