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We present a joint experimental and theoretical study of the superconducting phase of the layered binary silicide BaSi2. Compared with the AlB2 structure of graphite or diboridelike superconductors, in the hexagonal structure of binary silicides the sp3 arrangement of silicon atoms leads to corrugated sheets. Through a high-pressure synthesis procedure we are able to modify the buckling of these sheets, enhancing the superconducting transition temperature from 6 to 8.9 K when the silicon planes flatten out. By performing ab initio calculations based on density-functional theory we explain how the electronic and phonon properties are strongly affected by changes in the buckling. This mechanism is likely present in other intercalated layered superconductors, opening the way to the tuning of superconductivity through the control of internal structural parameters.