We present the first amplitude analysis of the decay Ds+→π+π0η. 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 Ds+→a0(980)+π0 and Ds+→a0(980)0π+. We measure the absolute branching fraction B(Ds+→a0(980)+(0)π0(+),a0(980)+(0)→π+(0)η)=(1.46±0.15stat±0.23sys)%, 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 Ds+→π+π0η with significantly improved precision.