La Roja opened their Group F campaign with a 2-1 success over Norway at the weekend and ensured that they would move onto six points in the section with a two-goal triumph on their travels.
Malta defended impressively for long spells of the contest, but a double from Alvaro Morata proved to be enough for the visitors to collect all three points.
Malta were without their most experienced defender through suspension, with Andrei Agius receiving a red card against the Faroe Islands at the weekend.
Zach Muscat for Agius was the change in central defence, but the nation's record goalscorer Michael Mifsud also dropped out as head coach Ray Farrugia switched to a 5-4-1 formation, with Joseph Zerafa and John Mintoff also coming into the XI.
As for Spain, only Sergio Ramos, Marco Asensio and Morata remained from the team that started the win over Norway at the weekend. Kepa Arrizabalaga replaced David de Gea between the sticks, while Sergi Roberto, Mario Hermoso, Jose Gaya, Rodri Hernandez, Sergio Canales, Saul Niguez and Juan Bernat all came into the side.
Malta's win over the Faroe Islands at the weekend proved to be their first success in a home competitive match for almost 13 years, but they never looked like upsetting Spain on Tuesday night.
Ramos had Spain's first half-chance in the fifth minute, but the Real Madrid defender headed a Canales free kick over Henry Bonello's crossbar as the visitors looked for the early breakthrough.
With Mifsud left on the bench, Kyrian Nwoko - who scored his first international goal at the weekend - led the line for Malta, but the Valletta attacker was left chasing shadows as La Roja continued to move the ball.
Saul sent one wide of Bonello's post in the 16th minute as the visitors had another sighter, before the Atletico Madrid midfielder fired over the crossbar from inside the box two minutes later.
Spain were, as expected, dominating the football, but the match approached its 25-minute mark with the score still goalless as Malta, and in particular the number four Steve Borg, continued to defend their lines.
Malta had completed less than 30 passes by the time the match reached 30 minutes, but the score remained level as Spain had little to show from their complete and utter dominance in terms of possession.
The breakthrough did arrive in the 31st minute, however, when Morata drove in the Maltese box before squeezing one through the grasp of Bonello, who might feel that he should have done better.
Saul again fired over the home side's crossbar in the 33rd minute before Asensio whipped a free kick too high six minutes later as Spain looked for a second, but Malta kept their heads and continued to defend well, with Joseph Mbong disciplined in a wide position as the two teams headed down the tunnel at 1-0.
Spain had 80% of the first-half possession, while they completed close to 450 passes, and it was not a surprise to see Luis Enrique's side immediately regain control of the ball at the start of the second period.
Malta have competed in every qualifier for the European Championships and World Cup, but have never managed to make it to the finals of a major international competition and face another huge task this time around.
The visitors had some half-chances in the early stages of the second period, but Asensio and Morata both had shots blocked, while Ramos could only hit the wall with a free kick from a dangerous position.
Morata then headed a Roberto cross wide of the post just before the hour, moments after Iker Muniain had been introduced in place of the disappointing Bernat.
Bonello had to make two smart saves to deny Asensio either side of the 60-minute mark as Spain looked for a second, but the 2010 world champions were still struggling to really force the issue.
Jesus Navas replaced the ineffective Saul for Spain in the 65th minute, while Rowen Muscat was brought on for a Maltese side who can be proud of their performance on the night despite only managing one shot on target.
Mifsud was introduced for the hosts in the 70th minute, but the game was put beyond Farrugia's side shortly after when Morata headed a pinpoint Navas cross into the back of the net for 2-0.
La Roja had a couple of half-chances to add to the scoring late on, but they were forced to declare at two as all three points were secured in unspectacular fashion against a Maltese side who had two long-range attempts in stoppage time through Nwoko and Mifsud.
Next up for Malta in Group F is a trip to Sweden on June 7, while Spain will be looking to make it three wins from three when they travel to the Faroe Islands on the same night.
MALTA (5-4-1): Bonello; Mbong (R Muscat 66'), Z Muscat, Caruana (Micallef 85'), S Borg, Zerafa; Corbolan, Guillaumier, Fenech, Mintoff (Mifsud 70'); Nwoko
SPAIN (4-3-3): Kepa; Roberto, Ramos, Hermoso, Gaya; Canales, Saul (Navas 65'), Rodri; Bernat (Muniain 56'), Morata (Rodrigo 79'), Asensio