French Olympic silver medallist, the top seed in her weight category, began her season in style with an ippon in the final
The Rio 2016 silver medallist, the top seed in the class, was pushed to golden score by Nabekura but triumphed after 2:41 of the extra period.
Agbegnenou's route to the final was nearly ended at the first hurdle after a first-round bye, as Britain's Lucy Renshaw pushed her to golden score before the Frenchwoman scored a waza-ari.
Japan's Ono Yoko, a two-time world champion in the mixed team event, fought her way to under-70 kg victory.
With world numbers one and two Marie-Eve Gahie and Margaux Pinot of France both suffering surprise early exits, only one of the world top five made it to the semi-finals in the Qatari capital.
That was world number three Sanne van Dijk, who lost to Ono in the semi-finals in the golden score period after receiving her third shido penalty.
Ono defeated Russia's Madina Taimazova in the final with a ne-waza takedown.
There was a shock in the men's under-73 kg final, as world number two and 2017 world champion Hashimoto Soichi was defeated by South Korea's An Chang-rim, his successor as world champion.
Hashimoto was penalised with a hansoku-make, only awarded for serious infractions of the rules, on an attempted waki-gatame armlock.
That awarded the victory to An by ippon by default.
Tato Grigalashvili of Georgia claimed victory in the men's under-81 kg. The recently-crowned European champion took down Frank De Wit of the Netherlands with a tomoe nage takedown to score an ippon win.
The Doha Masters concludes on Wednesday with the last five weight categories, including a return to action for a slim double Olympic champion Teddy Riner.