Real moved on to 21 points from eight games, one ahead of Barcelona, who beat Sevilla 1-0 at home on Friday. Girona dropped to third.
Real took the lead in the 17th minute through Joselu's simple finish after Bellingham played in a cross with the outside of his foot, before Tchouameni doubled the lead four minutes later when he cleverly wriggled free of his marker to head home a corner.
The win was wrapped up in the 71st minute when Joselu's looping pass found Bellingham, who deftly steered home a volley to score his seventh goal in all competitions for Real.
They suffered a setback, however, after a moment of madness from Nacho in added time as the defender leapt in with a high tackle on Portu, which was initially punished with a yellow card but overturned to red following a VAR review.
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