1.Global change, such as exotic invasions, dramatically affects ecosystem functioning. However, the mechanisms behind the impacts are often unclear and despite extensive experimental work, we know little about the importance of biodiversity loss as a component of global change effects in real‐world ecosystems. 2.We disentangled several mechanisms by which an exotic invader affected ecosystem functioning in East African drylands in Kenya and Ethiopia. We used structural equation modelling to separate direct effects of a woody invader (Prosopis juliflora) on a range of ecosystem functions from indirect effects mediated through changes in biodiversity (plant species richness) and ecosystem functioning (herbaceous biomass). We analysed effects on ecosystem functions linked to soil biogeochemical cycling and transfer of energy between trophic levels. 3.We found that the mean size of individual indirect effects mediated by biodiversity and herbaceous biomass was about twice as large as the mean size of individual direct effects of Prosopis on ecosystem functions, showing that indirect effects are an important component of the invader's overall environmental impacts. Changes in both herbaceous biomass and biodiversity were approximately equally important as drivers of indirect effects, indicating that we need to expand our view of indirect effects to consider a wider range of mechanisms. Simple univariate models failed to capture some Prosopis invader effects because positive direct effects on soil stability and predatory invertebrates were counteracted by negative indirect effects on biodiversity or biomass loss. The majority of effects were similar in both study systems. Suggestions that woody invaders are able to increase certain ecosystem functions may therefore have arisen because these negative indirect effects were not considered. 4.Synthesis Our study indicates that successful management of exotic invasions is likely to require not only control of the invader but also restoration of diverse and productive herbaceous communities as they are important for many ecosystem functions. This highlights the importance of biodiversity as a driver of ecosystem functioning also in real‐world systems.