The match was among four preliminary round first legs that began the process of qualifying 23 teams for the 2021 tournament, which Cameroon will host.
Should Sao Tome win the tie after the return match this Sunday in the tiny island nation off the coast of Gabon, they will join Ghana, South Africa and Sudan in Group C.
National team captain Leal plays for Rosario club Newell's Old Boys and having cancelled just before half-time the lead Kevin Perticots gave Mauritius, he struck again on the hour.
Jose da Silva added a third goal soon after to ensure the Saotomeans celebrated success after one draw and nine losses in away matches since debuting in the Cup of Nations against Togo.
Sao Tome may be ranked 190 of 210 countries, but their The Falcons and True Parrots nickname is among the most eye-catching in football.
The national squad comprises Leal, a handful of Portugal-based players, one who operates in Malawi and locals from first and second division sides.
When Sao Tome played a 2022 World Cup qualifier last month, they lost narrowly at home and away to 2017 and 2019 Cup of Nations qualifiers Guinea-Bissau.
Meanwhile, tiny east African nation Djibouti came agonisingly close to pulling off a second shock in as many months before being held 1-1 at home by the Gambia.
A Mohammed Mbye own-goal on 61 minutes put Djibouti ahead and they retained the lead until the first minute of stoppage time when Bubacarr Sanneh equalised.
Last month, Djibouti eliminated eSwatini (formerly Swaziland) from the race to fill five African places at the 2022 World Cup in Qatar.
French coach Julien Mette has swiftly transformed the Djiboutians from traditional whipping boys to competitive opponents, and is upbeat about The Shoremen of the Red Sea.
"The past is behind us," said the recently hired 37-year-old. "Personally, I do not remember the time when I was unable to walk. It took years but now it is in the past.
"It is the same for the Djibouti national team. New players, new coach, new methodology. The mentality of the players is naive and we are working on changing that."
Liberia edged Chad 1-0 in Paynesville through a Kpah Sherman goal while South Sudan beat the Seychelles 2-1 in a match moved to Sudan because the national stadium is being renovated.