Bellingham scored once and played a key role in another as Madrid quickly established control against Malaga, who have returned to the Spanish top flight after an eight-year absence.
The England midfielder, who also scored Madrid's opening goal of the season, once again broke the deadlock. Bellingham burst past two defenders before beating goalkeeper Alfonso Herrero from a tight angle, prompting supporters inside the stadium to serenade him with the Beatles' famous "Hey Jude".
He was involved again soon afterwards when his header turned a rebound from Kylian Mbappe's effort into the net, although the goal was eventually credited as an own goal after Malaga defender Carlos Pugas' attempted clearance struck Herrero and went in.
Mbappe then extended Madrid's advantage inside the opening half-hour, volleying home from Trent Alexander-Arnold's cross.
The goal marked Alexander-Arnold's first start at right-back this season after new signing Denzel Dumfries had started Madrid's opening two league matches.
Madrid continued to dominate after the interval, with Bellingham striking the post and going close on another occasion before substitute Arda Guler completed the scoring late on.
Vinicius Junior provided the assist for Guler, choosing to pass rather than attempt a shot himself as Madrid added further gloss to a comfortable victory.
Marc Cucurella also impressed on his first start since moving to Madrid from Chelsea.
Elsewhere in Spain, Deportivo La Coruna secured its first victory since returning to the top flight with a 3-1 win over Valencia, with Pierre-Emerick Aubameyang finding the net again.
Athletic Bilbao defeated Celta Vigo 2-0, leaving Celta without a win after three matches following an opening 0-0 draw against Valencia.
Barcelona are scheduled to face Rayo Vallecano on Monday.

Schalke suffer on Bundesliga return

Schalke's return to the Bundesliga after three seasons away began badly as they suffered a 3-0 defeat at Augsburg.
Gregoritsch opened the scoring before Schalke defender Ron Schallenberg was sent off for bringing down the striker with around half an hour remaining. Anton Kade and Rodrigo Ribeiro then completed the scoring for Augsburg.
Freiburg also enjoyed a convincing afternoon, defeating Werder Bremen 4-1.
Defending champions Bayern Munich had already made a powerful statement on Friday, beginning their title defence with a 5-1 victory over Stuttgart.

Como stun Napoli in Serie A

Como claimed an impressive 2-1 away victory over Napoli in a meeting between two clubs competing in the Champions League.
Tassos Douvikas and Martin Baturina scored for the visitors, with Rasmus Højlund briefly bringing Napoli back into the contest in the first half.
Inter Milan, meanwhile, needed another long-range strike from Hakan Calhanoglu to beat Cagliari 1-0. The midfielder had also scored from distance in Inter's opening 4-1 victory over Monza.

Brunner double lifts Monaco

Paris Brunner scored twice as Monaco defeated Marseille 2-0 at home to become the only team to open the Ligue 1 season with two victories.The German youth international headed Monaco ahead early before producing an impressive solo effort after the break, beating two defenders before finishing confidently.

Drama in Belgian derby

Gent handed Belgian champions Club Brugge their first defeat of the season, winning 2-1 through an 85th-minute header from Ibrahima Cisse.
The match ended with both teams down to 10 men. Brugge winger Carlos Forbs was dismissed before Cisse was also shown a red card in stoppage time for an elbow on an opponent.
Sporting Charleroi remain top after winning all four of their matches. (AP)