Andres Guardado, Hector Herrera and Carlos Vela shared the goals in the CONCACAF fourth qualifying stage Group A match at the Azteca stadium.
El Salvador, who last qualified for the World Cup in 1982, are rebuilding their side after 14 international players, including some of their best known and most experienced, were given life bans for match-fixing in September last year.
To add to their troubles, seven regular players were suspended by the Salvadorean federation last week for going on strike over working conditions and boycotting a training camp in October.
As a result, coach Ramon Maradiaga, appointed in September, was forced to call up a new squad made up largely of international novices.
Osorio became Mexico's 12th coach in the last 10 years when he was named to replace Miguel Herrera, the effervescent coach whose touchline celebrations and rantings made him a worldwide hit at the last World Cup.
Herrera was fired in July for allegedly punching a reporter who had criticised the team at Philadelphia airport in the United States. Brazilian Ricardo Ferreti took over on an interim basis until Osorio's appointment.
Guardado calmed early nerves with a beautiful, curling free-kick into the top corner in the seventh minute of the match following a foul on Javier Hernandez.
Herrera was credited with the second goal in the 42nd minute when he floated in a dangerous ball which made its way into the far corner with Hernandez's attempt to flick it home distracting El Salvador keeper Henry Hernandez.
Striker Vela completed the win after the break with a delicate chip over the advancing Hernandez.
"I'm keeping up my hope of qualifying for the World Cup with this group," Maradiaga told reporters. "We expected a defeat in this match but there were a lot of encouraging signs."
(Writing by Brian Homewood in Berne. Editing by Patrick Johnston)
