Bellingham beat three defenders before firing past Malaga goalkeeper Alfonso Herrero to open the scoring, and it was his header which then went in off Herrero, credited as an own goal, to make it 2-0.
Trent Alexander-Arnold then set up Kylian Mbappe to make it 3-0 with half an hour gone, and Arda Guler added a late fourth.
In Serie A, Inter Milan made it two wins from two to start the defence of their league title but had to hang on for a 1-0 win at Cagliari after squandering a string of chances.
Hakan Calhanoglu scored with their first real opportunity of the night 10 minutes in, but despite having a total of 30 attempts at goal on the night, Inter could not add to that and finished the night under pressure.
Lazio also got their second win as Davide Frattesi's 26th-minute strike earned a 1-0 win over Genoa, but Napoli were beaten 2-1 by Cesc Fabregas's Como.
Monaco ended the second weekend of Ligue 1 action as the only side still with a perfect record after Paris Brunner struck in either half to see off Marseille 2-0.
Paris FC picked up their first win of the campaign with a convincing 3-0 victory over Nice, starting with a 22nd-minute penalty from Lassine Sinayoko before second-half strikes from Samir Chergui and Vincent Marchetti.
In Germany, Japan's Yuito Suzuki hit a hat-trick as Freiburg started their campaign with a 4-1 win over Werder Bremen.
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