On an asymptotically conical manifold we prove time decay estimates for the flow of the Schrödinger, wave and Klein-Gordon equations via some continuity properties of the spectral measure. To keep the paper at a reasonable length we limit ourselves to the low energy part of the spectrum, which is the one that dictates the decay rates. With this paper we extend sharp estimates that are known in the asymptotically flat case (see Bouclet and Burq in [BB21]) to this more general geometric framework and therefore recover the same decay properties as for the euclidean case. The first step is to prove some resolvent estimates via a limiting absorption principle. It is at this stage that the proof of the previously mentioned authors fails, in particular when we try to recover a low frequency positive commutator estimate. Once the resolvent estimates are established we derive regularity for the spectral measure that in turn is applied to obtain the decay of the flows.