I’d say because of these two things:

• Obi-Wan actually surprisingly experienced this profound feeling of anger.

“Free at last of the laser wall, Obi-Wan Kenobi charged out of the service tunnel and into the chamber that housed the melting pit. Abandoning any pretense of observing even the slightest caution, he barreled into Darth Maul with such fury that he almost knocked both of them off the ledge and into the abyss. He struck at the Sith Lord with his lightsaber as if his own safety meant nothing, lost in a red haze of rage and frustration, consumed by his grief for Qui-Gon and his failure to prevent his friend’s fall.” ~ Star Wars: Episode I - The Phantom Menace (novelization)

Wow, and let me repeat again: “lost in a red haze of rage and frustration, consumed by his grief for Qui-Gon and his failure to prevent his friend’s fall.”

Kenobi was fueled by this ‘anger’—his own anger—because his master had died. His anger powered his body, which was why he was so fast paced at the very end of the duel with Darth Maul.

This was one reason. Second,

• Darth Maul became too arrogant.

After taking down one of the most respected Jedi Masters, Qui-Gon Jinn, this Sith Lord (Sith apprentice to be exact)—still being naive—thought he was invincible. All he had left was to deal with an inexperienced padawan learner, aka Obi-Wan.

He wasn’t truly ready to see Kenobi’s full potential and when it was lashed out at him, he was shocked.

He did regain his ground slightly throughout the battle, but ultimately, he thought he had won when Obi-Wan hanged from that elevator shaft. He couldn’t sense Obi-Wan’s trickery and ended up being cut in half at the hands of this very “inexperienced padawan learner.”

Overall, i’d say these were the two major reasons as to why Obi-Wan was able to defeat Darth Maul.