Rodrigo and Alcacer doubles seal victory against Faroe Islands
Captain Sergio Ramos equalled Iker Casillas' national appearances record with his 167th cap, but otherwise it was a low-key affair at El Molinon.
Spain now sit seven points clear in Group F after preserving their 100 percent record as second-placed Sweden were held to a 1-1 draw by Norway.
There was a minute's silence before the game in tribute to former coach Luis Enrique's daughter Xana who died of bone cancer aged nine last week.
Robert Moreno, who took over as boss from Enrique when the ex-Barcelona coach stepped down in June, made 10 changes to the starting XI which won 2-1 in Romania on Thursday, with only Ramos keeping his place.
The hosts wasted little time in taking the lead as the Faroes buckled under intense pressure in the 13th minute, missing several chances to clear the ball before Mikel Oyarzabal set up Rodrigo for a simple tap-in despite suspicions of offside.
Spain struggled to break down their stubborn opponents for the rest of the first half, though, despite away goalkeeper Gunnar Nielsen being forced into an excellent save to keep out Thiago Alcantara's spectacular long-range volley.
But Valencia striker Rodrigo put the game to bed five minutes into the second half, cutting inside from the right and drilling a vicious left-footed strike into the top corner with the aid of a deflection.
Despite having failed to score for his club so far this season and only managing eight goals in La Liga last term, the 28-year-old has netted five times in nine competitive internationals since the 2018 World Cup.
Joannes Bjartalid gave Spain a scare with quarter-of-an-hour to play, but David de Gea denied him a famous goal with an excellent save.
Instead, substitute Alcacer came off the bench to slot in Thiago's low cross in the 90th minute, before the Borussia Dortmund forward flicked in a near-post header to score his third Spain goal this week.