Anakin was able to beat him because he became angry and used a side of the force (dark through his anger amplified by Sidious who was urging him on) which was more powerful and could overcome Dooku who was overly confident, probably not expecting to lose this time around either and ultimately caught of guard.
The relationship between Sith Apprentice Count Dooku and Jedi Knight/General Anakin Skywalker is one of the main enmity relationships seen in Star Wars: The Clone Wars. Anakin has a personal vendetta against Dooku because he had dismembered Anakin's limb and cuased him to get a mechanical arm.
So he's old, and nearly old enough to be an invalid. During that scene, Anakin keeps getting egged on by Palpatine, who repeatedly tells Anakin to kill him. Eventually, he succumbs to his anger and rage and uses the Dark Side to defeat Count Dooku.
Anakin regrets this decision, and Palpatine reasons with him saying that Dooku was too dangerous.
When Dooku was still with the Jedi Order, he was considered to be one of the greatest (if not the greatest) lightsaber duelists of his generation. Anakin really wasn't as good of a duelist as many people hype him up to be.
Like many of the other Sith, Count Dooku was incredibly proficient with the Force, even being able to win a fight against Yoda. Despite this, though, he still wasn't the best fighter with a lightsaber, and his Force skills were not nearly as powerful as Darth Vader's.
1 Darth Sidious
There has been no Sith, as powerful, meticulous, nor as evil as the Emperor himself, Darth Sidious. As previously mentioned, Sidious trained in the Dark Side by Darth Plagueis before Sidious killed Plagueis in his sleep, making Sidious a Sith Master.
This is confirmed later in the movie when Obi-Wan informs Padme that Anakin killed them. Both are torn apart with hurt and confusion, trying to make sense of something so terrible.
In legends, Dooku actually explains why he hates Anakin: He could feel Yoda's touch still lingering on the edges like a distant echo. Vividly his mind went back to their last meeting, on Geonosis: swords drawn at last, and finally equal.
His best friend had been given a gift that could have allowed the Jedi to help countless people, but Yoda refused to act. As a Jedi, Dooku couldn't stand the thought that his best friend was suffering without a purpose, so he hated Yoda and the Jedi Order for that. In the end, though, Yoda was right.
Bottom line, Dooku never considered himself a Sith. And he wasn't; he was a man looking to change the galaxy in a way the Jedi were unwilling to try. And that is why he joined the Sith and became Darth Sidious' apprentice, Darth Tyrannus. When Dooku became Sidious's apprentice, he was already an elderly man.
Anakin Skywalker
During that battle, he learned why Qui-Gon supported and defended Anakin, when he showed how strong his connection to the Force is. Dooku had very little respect for the young Jedi Knight, despite his bravery and unbelievably strong connection to the Force.
A former Jedi Master, Dooku had lost faith in the Republic and in the Jedi, believing them to be too tied to a corrupt political institution. He left the Jedi and fell under the sway of Darth Sidious, apprenticing to him in the hopes of bringing peace and order to the galaxy.
Obi Wan was unable to defeat Count Dooku because the Count was a significantly better lightsaber duelist. Obi Wan was a master in Form III lightsaber combat. Form III is an almost entirely defensive style of combat. Obi Wan was essentially a diplomat before the Clone Wars.
Revenge of the Sith (2005)
Anakin gives in to his hatred of Dooku and uses his anger to overpower him, severing both of Dooku's hands and leaving him helpless.
The attempt was carried out by Zam Wesell, a partner of bounty hunter Jango Fett who himself following orders from Count Dooku, leader of the Confederacy of Independent Systems so that it could gain the backing of Nute Gunray and the Trade Federation under the condition that Amidala was killed.
Had Anakin not converted: Padme would have been killed by the Emperor before childbirth, and before Anakin and Obi wan returned from the mission to destroy general Grievous. Regardless: order 66 probably still would have happened since the army was under control of the dicator in Palpatine.
Anakin admits to Obi-Wan that he has been arrogant and unappreciative of his training, and apologizes to his master. Obi-Wan assures Anakin that he is proud of him, telling him that he has become a "far greater Jedi than I could ever hope to be."
We go for the more simple answer, further considering the details of the question itself. If Anakin didn't go into that chamber as the Jedi confronted Palpatine, then Mace Windu would have defeated Palpatine, killing him.
Anakin does not have even the slightest bit of remorse. By the end, he feels nothing but anger. Although he feels regret for killing Padme, he still helps the evil Emperor. The film ends with Anakins standing side by side with the man on whose behalf he has committed all his crimes.
The story is Anakin was manipulated to the dark side by Palpatine based on fears of losing Padme and appeals to his desire power and agency, over his life and the galaxy as a whole.
“The tear [on Anakin's face] says that he knows what he's done, but he has now committed himself to a path that he may not agree with… but he is going to go on anyway. It's the one moment that says he's self-aware that he's rationalizing all his behavior.
Darth Sidious was also one of the greatest and most skilled Sith swordmasters, as he has mastered all the seven lightsaber forms, all their stances and techniques and is capable of using each form equally effective ambidextrously.
Biography. Legend had it that Yoda—a Jedi who became Grand Master—was trained by N'Kata Del Gormo.
Master Yoda has risen above all others to claim the top spot as the most powerful Jedi of all time and the true chosen one according to IGN's audience. He won pretty handily as well, as he was victorious in 89,756 of his 95,243 battles and had a win percentage of 94.2%.