Mexico scored further goals through midfielder Carlos Pena and strikers Oribe Peralta and Jesus Escoboza with Finland hitting back through Jarkko Hurme and an own goal by defender Juan Carlos Valenzuela.
Mexico meet New Zealand over two legs, at home on November 13 and away a week later, for a berth at the 2014 finals in Brazil.
"I'm very satisfied and happy with the team's performance and although we must correct errors that brought goals (for the opposition) the team showed a clear idea of what we want on the pitch," Herrera said.
"I find the team ready in their minds, a win like this helps to gain confidence," Herrera, Mexico's fourth coach in less than two months, told reporters.
He fielded seven players from his club side America, the Mexican champions and league leaders, looking for the stability lacking in the team when they failed to qualify directly from the CONCACAF final group this month.
(Reporting by Carlos Calvo in Mexico City; Writing by Rex Gowar)
