Another mistake by match officials created controversy and helped Argentina reach the quarter-finals of the World Cup in Johannesburg on Sunday.
After England had a goal not given earlier in the day against Germany despite the ball having crossed the line, Argentina benefited in their last-16 match against Mexico with one that should have been disallowed.
Carlos Tevez was the nearest to goal when he headed Argentina's opener in the 26th minute in Johannesburg's Soccer City Stadium after taking a pass from Lionel Messi.
Italian assistant referee Stefano Ayroldi did not raise his flag and the goal was allowed to stand after discussions with referee Roberto Rosetti, despite protests from the Mexicans.
Argentina players then joined in the protests when it appeared the goal would be disallowed, as everyone in the stadium who had watched replays on the huge screens could see that Tevez was clearly offside.
Despite this - and because technological aids are not allowed - the goal was allowed to stand, although it was unclear whether the officials had seen the replays.
"Before today I was not an advocate of technology in football, but now I am a convert," former Scotland international and BBC pundit Alan Hansen said.
Argentina went on to win 3-1 thanks to goals from Gonzalo Higuain following a mistake by Ricardo Osario and a Tevez thunderbolt from outside the area seven minutes after the break before Javier Hernandez rifled one back for Mexico.
The victory sets up a quarter-final against Germany in Cape Town Saturday. The two sides met at the same stage at the 2006 World Cup in Germany when Argentina went out in a penalty shoot-out.
England midfielder Frank Lampard called earlier for football to adopt technology to avoid errors similar to the one that saw his goal not given during England's 4-1 defeat to Germany Sunday.
Lampard said he did not need to watch television replays of the incident to know the goal should have been allowed.
"I knew straight away that it was over the line ... clearly by a yard or so," he said of his blast, which hit the underside of the crossbar and then bounced downwards over the line and out again.
Before the World Cup, players had been told about "a million different rules and changes that hardly affect the game", Lampard said.
"But the big one that affected the game today hasn't been brought in," Lampard said, referring to goal-line technology.
Football's governing body, FIFA, has steadfastly refused to install sensors and other technology-assisted measures.