Appearing at his fourth World Cup, man-of-the-match Marquez opened the scoring in the 72nd minute, powering home a header from a corner and turned provider 10 minutes later, flicking on for an unmarked Javier Hernandez to head into an empty net.
Andres Guardado had added a second three minutes after the Marquez strike as Croatia chased the victory they needed to qualify.
"I called him [Marquez] and asked him to be captain and the leader of our team," said an elated Herrera, who took over as Mexico manager in October.
"We needed a leader who is concentrated, involved, commanding, screaming, shouting, giving my instructions on the field," he told a news conference. "I did not hesitate to appoint him captain. I had no doubt that he was number one in the list of 23.
"He has given leadership in the group, that's why they call him 'the boss' in the group."
The victory gave Mexico second spot in Group A on seven points with hosts Brazil topping the standings on goal difference following a 4-1 victory over Cameroon.
Feel-good factor back for Brazil
World Cup morale is high once again in Brazil, according to superstar Neymar, after the hosts finally clicked into gear to secure top spot in Group A with a 4-1 victory over hapless Cameroon.
A swashbuckling attacking display in Brasilia in the Cameroon romp ensured Brazil finished above Mexico in the final standings so they avoid in-form Netherlands in the second round.
"The most important thing was the team and I think this was our best performance," said Neymar, 22, whose brace took him to the top of the World Cup scoring charts on four.
Meanwhile, Brazil coach Luiz Felipe Scolari said his team are getting better all the time.
"We have qualified but it wasn't easy,” he said. “Cameroon are a good side and it is hard to see how they could have lost three games when you see how they played.
"We are almost at the ideal level and it is important coming into the knockout phase.”
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