Luka Modrić's 85th minute equaliser and Bellingham's stoppage time winner on Friday ensured Madrid avoided back-to-back defeats in La Liga for the first time since 2019.
The win took them to 43 points, two above city rivals Atletico, albeit having played a game more.
The match at the Mestalla pitted second from bottom against second from top and it was the struggling home side who took the lead after 27 minutes. Hugo Duro stabbed the ball into the empty net after it came back off the post.
Madrid came into the game more in the second half but it looked like it would be a frustrating night for the capital club.
Kylian Mbappé won a penalty after 55 minutes but Bellingham's shot hit the post and moments later the Frenchman himself saw a goal disallowed after a video review.
Things got worse for Real with 11 minutes remaining when Vinicius Jr. pushed goalkeeper Stole Dimitrievski and the referee, after a long video review, showed the Brazilian a red card.
However, Real were never out of it and Carlo Ancelotti's late changes turned the game around.
Modrić came on in the 80th and it took the 39-year-old Croatian just five minutes to make his mark, dancing through a sea of defenders and poking home the equaliser.
Even with a man less there was a sense of inevitability as Real pushed for a winner, and five minutes into added time Bellingham made up for his earlier miss.
Valencia defender Hugo Guillamón seemed to slip and lay the ball into the path of the advancing Englishman, who made no mistake with only the keeper to beat.
Even then the drama was not over. Valencia deserved to take something from the match and Luis Roja almost got an equaliser with the last kick of the game. He watched in agony as his long-range shot came back off the post.
In the Spanish Cup, fourth-tier side Pontevedra have slain high-flying La Liga side Mallorca 3-0 to move into the last 16.
Dalisson de Almeida scored from almost 40 yards to make it 1-0 after 21 minutes, Yelko Pino doubled the lead with a cracking volley four minutes into the second half, and then Rufo rounded off the perfect night with 18 minutes left after a shocking defensive lapse.
The Galician side knocked out Villarreal in the last round.
In the night's other games, top-tier clubs Rayo Vallecano and Getafe progressed.
Getafe needed extra time to beat second-division Granada in southern Spain. After a goalless match, Borja Mayoral got the only goal in the 93rd minute to put the visitors through.
Rayo Vallecano made swift work of second-tier Racing Ferrol. Alfonso Espino and Jorge de Frutos put the visitors 2-0 up before half-time and Frutos grabbed a third on the hour mark.
Álvaro Giménez scored a late consolation for the hosts.
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