Oribe Peralta's second-half goal sent Mexico through with a 1-0 win over Switzerland, which eliminated the Swiss. Honduras squeezed into the last eight with a 0-0 draw against already qualified Japan - although they may struggle to get any further.
Honduras will next take on big favorite Brazil, which had qualified for the quarterfinals even before beating New Zealand 3-0 for a third straight win.
The last two spots in the knockout round were to be decided later Wednesday, when Senegal played already eliminated United Arab Emirates and Britain faces Uruguay. Senegal and Britain have four points each and Uruguay has three.
South Korea also only needed a scoreless draw to advance, against Gabon in front of 76,927 spectators at Wembley.
Mexico will play at Wembley next, and is hoping it will continue to improve as the tournament progresses.
"We have been growing in confidence and now we have won two matches in a row which is something very positive," Mexico defender Carlos Salcido said. "Now we will wait to see who our rivals are going to be and we will go for the win, as we always do."
Switzerland, which was playing without Michel Morganella after the defender was sent home for posting racist and threatening messages on Twitter against South Koreans, finished last with one point in the group behind Gabon.
Brazil coach Mano Menezes rested several of his key players, but that didn't stop Danilo and Leandro Damiao from scoring before halftime. Alex Sandro added the third at St. James' Park in Newcastle, where the team will stay for its quarterfinal. Brazil finished with 10 men after Sandro received his second yellow card in the 76th.
"We're getting stronger as the competition goes on," Brazil defender Rafael said. "Brazil always has to think of a medal. The next stage is important, if we lose, we're out. We need concentration and focus."
Egypt advanced after beating Belarus 3-1 to finish second behind Brazil in Group C with four points. In Glasgow, Mohamed Salah, Marwan Mohsen and Mohamed Aboutrika all scored second-half goals for Egypt before Andrei Voronkov netted a late consolation goal for Belarus, which was eliminated.
All quarterfinals matches will be played on Saturday.
(For more sports news and updates, follow Ahram Online Sports on Twitter at @AO Sportsand on Facebook at AhramOnlineSports)