We show that stochastic acceleration can be achieved under the perturbed iterate framework (Mania et al., 2017) in asynchronous lock-free optimization, which leads to the optimal incremental gradient complexity for finite-sum objectives. We prove that our new accelerated method requires the same linear speed-up condition as existing non-accelerated methods. Our key algorithmic discovery is a new accelerated SVRG variant with sparse updates. Empirical results are presented to verify our theoretical findings.