Dani Olmo turned in Alejandro Balde's driven low cross on 13 minutes in Malaga and Joselu scored twice on his Spain debut to give new coach Luis de la Fuente a victory in his first match in charge.
Chelsea goalkeeper Kepa Arrizabalaga pulled off a brilliant reflex stop to deny Fredrik Aursnes and clawed another effort off the line on his first start for Spain since October 2020.
Alexander Sorloth then volleyed wide before Espanyol striker Joselu came off the bench and bagged a quick-fire double -- heading in his first and sweeping home a rebound for the second.
Three-time European champions Spain next go to Scotland, who saw off Cyprus 3-0 in their Group A opener after Scott McTominay scored twice late on as a substitute at Hampden Park.
Cyprus finished with 10 men after Nicholas Ioannou was sent off for a second yellow in added time.
"It's a really good start but we have to try and back it up on Tuesday against the Spanish," said Scotland manager Steve Clarke.
Norway, who haven't played at a major tournament since Euro 2000, will again be without Manchester City striker Haaland for next week's trip to Georgia because of a groin problem.
Croatia, finalists and semi-finalists at the past two World Cups, conceded a last-gasp equaliser to kick off Group D as Wales debutant Nathan Broadhead tapped home a flick-on from a long throw.
Andrej Kramaric's low shot from just outside the area had given Croatia the lead in Split against a Wales team beginning life after the retirement of their record goalscorer and captain Gareth Bale.
Luka Modric won his 163rd cap for Croatia, who have never lost a home European Championship qualifier -- a run now spanning 36 matches dating back to 1994.
Turkey came from behind to defeat Armenia 2-1 in Yerevan as efforts from Orkun Kokcu and Kerem Akturkoglu cancelled out an early own goal by former Liverpool defender Ozan Kabak.
Renato Steffen scored a first-half hat-trick as Switzerland thrashed Belarus 5-0 in a game played behind closed doors in Serbia.
UEFA has banned Belarus from playing at home due to the country's support for the Russian invasion of Ukraine.
Granit Xhaka and Zeki Amdouni, on his second international appearance, added goals in the second half as Switzerland powered top of Group I.
Dennis Man and Denis Alibec were on target as Romania eased to a 2-0 win away to 10-man Andorra.