They put their money where their mouth
Unlike Microsoft, Google committed fully to Android and provided regular updates. Even if the updates often never reached the customers, the manufacturers appreciated them as the approach fitted the new phone every two years model. This is why "fragmentation" featured only in tech articles: people were used to buying new phones.
The AOSP model also worked for them here: while Google released a flagship every year, the other manufacturers were quickly able to follow up with their own phones. But if AOSP was great for the manufacturers, it was Play Services and Gapps wot won it as they provided compelling arguments and, of course, ad-supported apps using the world's largest digital ads platform appealed to lots of developers.
Google's commitment to AOSP shouldn't be underrated. All the time it was pushing Android it was also pushing "open", enabling technologies such as WebM and HTML5, which made moving between platforms (desktop, mobile, web, Android, I-Phone) fairly easy: a torus not a walled garden.