The former Real Madrid goalkeeper had not played for Costa Rica since last year's World Cup in Qatar, missing a couple of friendlies and the CONCACAF Gold Cup in July.
The Central Americans took the lead in the 12th minute when defender Francisco Calvo headed home Joel Campbell's cross.
Manfred Ugalde made it 2-0 just past the half-hour mark with another header in the six-yard box from Jimmy Marin's pass.
Saudi Arabia, who are now managed by former Italy coach Roberto Mancini, pulled one back in the 68th minute when Ali Al Bulayhi headed in Feras Al Brikan's pass from a corner.
However, they could not find the equaliser and Costa Rica wrapped up the win when Randall Leal fired home in the 89th.
Costa Rica face the United Arab Emirates in a friendly in Croatia on Tuesday, while Saudi Arabia play South Korea back at Newcastle United's home ground.
