We present the first amplitude analysis of the decay D-s(+) -> pi(+)pi(0)eta. We use an e(+)e(-) collision data sample corresponding to an integrated luminosity of 3.19 fb(-1) collected with the BESIII detector at a center-of-mass energy of 4.178 GeV. We observe for the first time the W-annihilation dominant decays D-s(+) -> a(0)(980)(+)pi(0) and D-s(+) -> a(0)(980)(0)pi(+). We measure the absolute branching fraction B(D-s(+) -> a(0)(980)(+(0))pi(0(+)), a(0)(980)(+(0)) -> pi(+(0)())eta = (1.46 +/- 0.15(stat )+/- 0.23 sys)%, which is larger than the branching fractions of other measured pure W-annihilation decays by at least one order of magnitude. In addition, we measure the branching fraction of D-s(+) -> pi(+)pi(0)eta with significantly improved precision.