In many species, oocyte meiosis is carried out in the absence of centrioles. As a result, microtubule organization, spindle assembly, and chromosome segregation proceed by unique mechanisms. Here, we report insights into the principles underlying this specialized form of cell division, through studies of C. elegans KLP-15 and KLP-16, two highly homologous members of the kinesin-14 family of minus-end-directed kinesins. These proteins localize to the acentriolar oocyte spindle and promote microtubule bundling during spindle assembly; following KLP-15/16 depletion, microtubule bundles form but then collapse into a disorganized array. Surprisingly, despite this defect we found that during anaphase, microtubules are able to reorganize into a bundled array that facilitates chromosome segregation. This phenotype therefore enabled us to identify factors promoting microtubule organization during anaphase, whose contributions are normally undetectable in wild-type worms; we found that SPD-1 (PRC1) bundles microtubules and KLP-18 (kinesin-12) likely sorts those bundles into a functional orientation capable of mediating chromosome segregation. Therefore, our studies have revealed an interplay between distinct mechanisms that together promote spindle formation and chromosome segregation in the absence of structural cues such as centrioles.