It was a straightforward win that took Spain on to a maximum 18 points after six games and leaves them seven ahead of second-placed Sweden, who drew 1-1 at home to Norway.
Spain homed in on Euro 2020 by easing past the Faroe Islands 4-0 on Sunday for a sixth straight qualifying win that featured two goals each from Rodrigo and Paco Alcacer and moved them further clear at the top of Group F.
Sergio Ramos equalled Iker Casillas' record of 167 appearances for Spain on an emotional night at Sporting Gijon's El Molinon stadium, which paid tribute to the late Spain and Sporting forward Quini before kick off.
A minute's silence was also held in memory of former Spain coach Luis Enrique's daughter Xana, who passed away last month.
There followed a straightforward win that took Spain on to a maximum 18 points after six games and leaves them seven ahead of second-placed Sweden, who drew 1-1 at home to Norway.
Romania beat Malta 1-0 with a goal from George Puscas to leapfrog Norway into third place on 10 points.
Valencia striker Rodrigo tapped into an empty net to put Spain in front in the 13th minute despite being in an offside position when he received a pass from Mikel Oyarzabal.
But with video technology not in use in the qualifying phases, the goal stood.
Rodrigo doubled Spain's lead in the 50th minute on coach Robert Moreno's home debut by cutting in from the right wing and firing a left-footed shot towards goal which took a heavy deflection off a visiting defender on its way into the net.
Alcacer then entrenched his reputation as a highly productive substitute by further stretching Spain's advantage with simple strikes in the 89th minute and deep in stoppage-time.
Midfielder Thiago Alcantara said the team had not played as well as they would have liked due to the visitors' negative tactics.
"It was very tough at first, you expect a team like them to close you down and sit back and that's what happened and we struggled to break them down," he said.
"They had three players marking one of ours although once we got the first goal it was slightly easier. We still weren't completely comfortable but we're happy with the result."
With the top two sides in each group guaranteed a place at Euro 2020, Spain need only win two of their remaining four games to qualify for the tournament, but Thiago said his side were determined to win every match.
"We are focused on getting all the points, it doesn't matter to us when we qualify, we want every point, from the first to the last," he added.