Mexico's all-time leading goal scorer Javier Hernandez pulled one back for his side with a classic flying-header in the 42nd minute with both teams going into the break 1-1.
The match kicked off in Kazan after a moment of silence in memory of the victims who have died in forest fires in Pedrogao Grande, Portugal.
A moment of controversy came when Pepe's goal was ruled out in the 21st minute after there were appeals Nani was offside.
"The team had nearly won and we suffered in the last minute, but this is football".
The former Manchester United forward capitalised on Carlos Salcedo misjudging a header just inside his own half to race into the penalty area and, given too much time to turn, the Portugal captain was able to easily pick out the unmarked Quaresma, who deceived Guillermo Ochoa with his first touch and slotted home with his second.
Ronaldo made a great run from near midfield to set up Quaresma's 34th-minute goal. Mexico midfielder Carlos Vela got to the ball near the far post and sent it to the middle of the area for Chicharito's goal.
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Portugal ended 2-2 with Mexico and, perhaps fortunately for FIFA, Chile beat Cameroon 2-0.
But Portugal's celebrations were premature as Moreno popped up with the equaliser.
"It wasn't the result that we wanted", he said. "But we are not anxious, there are two games left, we still have chances". Now we need to think of the next game, which we have to win.
One "clear error" might be overturned every four or five games, Federation Internationale de Football Association head of refereeing Massimo Busacca suggested previous year.
"We do not have to sound the alarm".
"We know we didn't play well", he said. "We faced the European champions, a team that plays at a very high level, and we played equal to them".
"At the start we couldn't enjoy good control of the ball but then we managed to balance things out and could have won it. It was a fair result for how the teams played".