Mexico striker Javier Hernandez cancelled out Quaresma's opener shortly before halftime and the two goals in an exciting last six minutes ensured the teams shared the points.
Whether it was the right flank in the first half or the left in the second half, Quaresma was quite easily the most menacing of attacking players for Portugal ahead of the much fancied Ronaldo.
Ronaldo and Zidane will reportedly hold further talks at the end of the Confederations Cup, but, for now, the player is keeping his own counsel after not appearing at the post-match press conference following Portugal's opening game of the tournament.
His 30-metre strike bounced off the bar and Nani hammered the ball home but the referees disallowed the effort for an offside infringement earlier in the move.
With the game looking like it may end deadlocked at 1-1 defender Cedric popped up in the box to fire home his first worldwide goal via a deflection.
Cristiano Ronaldo is not letting accusations of tax fraud and fresh transfer speculation get to him, according to Portugal team-mate Andre Silva.
European champions Portugal, captained by the relentless Cristiano Ronaldo, will look to build on their success in France last summer and prove that they are also contenders for the Tournament of Champions and next year's World Cup in Russian Federation.
But with the 90 minutes up, Mexican defender Moreno rose highest from the final corner of the game to head in the equaliser.
'The team continue to believe in qualification, we have great possibilities, because there are still two games left'. "I think that we communicate well and we have a good understanding, and that leads to these good results".
"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". If you bring benefits to football, fine, ' he added.
As Bleacher Report noted, the match could be something of an uphill climb for El Tri as they face one of the best-playing teams in the world right now.
'It's the new rule.