The winless visitors took a shock 2-0 lead at the Bernabeu with goals from Largie Ramazani and Edgar Gonzalez.
England midfielder Bellingham scored a 57th-minute penalty, before Vinicius Jr equalised 10 minutes later.
In the ninth minute of added time, Bellingham headed across for Dani Carvajal to poke in the winner.
The dramatic victory briefly took Real top, but Girona moved back to the summit with a 5-1 victory over struggling Sevilla later on Sunday.
Ukraine striker Artem Dovbyk scored a hat-trick for the surprise leaders to join Bellingham as La Liga’s joint-top scorer on 14 goals.
Speaking about Real’s win, Almeria midfielder Gonzalo Melero told DAZN “we were robbed” after several Video Assistant Referee (VAR) decisions went against his team.
“It pains me to say it, but there’s no other way to take it,” he added. “And that’s not the first this year. What happened today went beyond all limits, it was unbelievable.
“Nothing more could have been done for them to win the game.”
Goalscorer Gonzalez added: “This is a competition that should be fair for everyone and sometimes it’s hard to see that.”
Real were expected to brush aside an Almeria side who have picked up just a solitary point on the road in a miserable 2023-24 campaign.
But on the back of a goalless draw at home to Girona last time out, the Andalusian outfit stunned the hosts with a goal after 38 seconds.
Neat build-up play after they pinched possession allowed Lucas Robertone to slip in the unmarked Ramazani and his low effort wrong-footed Kepa Arrizabalaga.
Gonzalez’s sweetly-struck half-volley in the 43rd minute then flew over a flat-footed Kepa to increase Almeria’s advantage.
But Real were awarded a debatable penalty after the VAR decided the ball had brushed the arm of Kaiky, with Antonio Rudiger deemed not to have committed a foul in the build-up.
Bellingham stepped up to net his first La Liga spot-kick as he confidently sent Almeria goalkeeper Luis Maximiano the wrong way.
Almeria thought they had a third when Sergio Arribas slotted the ball past Kepa from Ramazani’s cross but the VAR overruled it.
Vinicius Jr then levelled with another controversial goal, which was initially ruled out for handball after the Brazilian appeared to guide it in with his arm.
However, the referee reviewed it on the pitchside monitor and overturned his original decision.
Almeria boss Gaizka Garitano was sent off for a second booking for dissent as Real snatched a winner in the ninth of 11 minutes of injury time.
A deep cross from a Real counter-attack picked out Bellingham who directed his header to the opposite side of the six-yard box where Carvajal applied a close-range finish.
“I understand Almeria’s anger with the VAR decisions, but I think they were well judged,” said Real boss Carlo Ancelotti.
“It was a strange game, the first half was very bad. I judged yesterday’s training session poorly, it was a tired team.”
