Using a sample of 448.1×106 ψ(3686) events collected with the BESIII detector, we perform a study of the decay ψ(3686)→φπ+π-η. The branching fraction of ψ(3686)→φη′ is determined to be (1.51±0.16±0.12)×10-5, which is consistent with the previous measurement but with significantly improved precision. The resonances f1(1285) and η(1405) are clearly observed in the π+π-η mass spectrum with statistical significances of 18σ and 9.7σ, respectively. The corresponding product branching fractions are measured to be B(ψ(3686)→φf1(1285), f1(1285)→π+π-η)=(1.03±0.10±0.09)×10-5 and B(ψ(3686)→φη(1405), η(1405)→π+π-η)=(8.46±1.37±0.92)×10-6. These results are used to test the perturbative QCD "12% rule."