A strong 50–35 Ma decrease in India‐Asia convergence is generally ascribed to continent‐continent collision. However, a convergence rate increase of similar magnitude occurred between ∼65–50 Ma. An earlier increase occurred at ∼90 Ma. Both episodes of accelerated convergence followed upon arrival of a mantle plume below and emplacement of a large igneous province (LIP) on the Indian plate. We here first confirm these convergence rate trends, reassessing the Indo‐Atlantic plate circuits. Then, using two different numerical models, we assess whether plume head arrival and its lateral asthenospheric flow may explain the plate velocity increases and whether decreased plume flux and increasing continent‐plume distance may explain deceleration, even without continental collision. The results show that plume head arrival can indeed lead to absolute Indian plate motion accelerations on the order of several cm/yr, followed by decelerations on timescales similar to the reconstructed fluctuations. The 90 Ma increase could potentially be explained as response to the Morondova mantle plume alone. The 65–50 Ma convergence rate increase, however, is larger than can be explained by plume head spreading alone. We concur with previous hypotheses that plume‐induced weakening of the Indian continental lithosphere‐asthenosphere coupling and an increased slab pull and ridge push efficiency are the most likely explanations for the large convergence rate increase. The post‐50 Ma decrease is best explained by orogeny‐related increased trench resistivity, decreased slab pull due to continental subduction, and possibly restrengthening of lithosphere‐asthenosphere coupling upon plume demise. Key Points India‐Asia plate convergence underwent strong acceleration and deceleration These cycles relate to arrival of mantle plumes below India The strong deceleration around 50 Ma probably relates to India‐Asia collision