[en] We present a precise calculation of the dilepton invariant-mass spectrum and the decay rate for B^±→π^±l⁺l^- (l^±=e^±,μ^±) in the Standard Model (SM) based on the effective Hamiltonian approach for the b→dl⁺l^- transitions. With the Wilson coefficients already known in the next-to-next-to-leading logarithmic (NNLL) accuracy, the remaining theoretical uncertainty in the short-distance contribution resides in the form factors f₊(q²), f₀(q²) and f_T(q²). Of these, f₊(q²) is well measured in the charged-current semileptonic decays B→πlν_l and we use the B-factory data to parametrize it. The corresponding form factors for the B→K transitions have been calculated in the Lattice-QCD approach for large-q² and extrapolated to the entire q²-region using the so-called z-expansion. Using an SU(3)_F-breaking Ansatz, we calculate the B→π tensor form factor, which is consistent with the recently reported lattice B→π analysis obtained at large q². The prediction for the total branching fraction B(B^±→π^±μ⁺μ^-)=(1.88_+0.32^-0.21) x 10^-8 is in good agreement with the experimental value obtained by the LHCb collaboration. In the low q²-region, the Heavy-Quark Symmetry (HQS) relates the three form factors with each other. Accounting for the leading-order symmetry-breaking effects, and using data from the charged-current process B→πlν_l to determine f₊(q²), we calculate the dilepton invariant-mass distribution in the low q²-region in the B^±→π^±l⁺l^- decay. This provides a model-independent and precise calculation of the partial branching ratio for this decay.