We study the rare hadronic transitions Y(2S) -> Y(1S)eta and Y(2S) -> Y(1S)pi(0) using a sample of 158 x 10(6)Y(2S) decays collected with the Belle detector at the KEKB asymmetric-energy e(+)e(-) collider. We measure the ratios of branching fractions (B) B(Y(2S)-> Y(1S)eta)/B(Y(2S)-> Y(1S)pi(+)pi(-)) = (1.99 +/- 0.14(stat) +/- 0.11(syst) x 10(-3) and B(Y(2S)-> Y(1S)pi(0))/B(Y(2S)-> Y(1S)pi(+)pi(-)) < 2.3 x 10(-4) at the 90% confidence level (CL). Assuming the value B(Y(2S)-> Y(1S)pi(-)pi(+)) = (17.92 +/- 0.26)%, we obtain B(Y(2S)-> Y(1S)eta) = (3.57 +/- 0.25(stat) +/- 0.21(syst)) x 10(-4) and Y(2S) -> Y(1S)pi(0) < 4.1 x 10(-5)(90%CL). DOI: 10.1103/PhysRevD.87.011104