This paper studies monetary policy design in small open economies with cross-border and input-output linkages. We derive the divine coincidence (DC) Phillips curve linking the output gap to a DC index that weights each sector's inflation by sectoral contents in domestic consumption and exports, and of domestic labor. Output gap targeting can be implemented by stabilizing the DC index, which assigns larger weights to sectors that supply more inputs directly or indirectly to domestic output and face larger expenditure-switching effects. Disregarding openness or treating the economy as one sector overemphasizes inflation in sectors that export directly or indirectly, and underemphasizes inflation in sectors facing large expenditure-switching effects. We quantify our theoretical results using the World Input-Output Database, showing that the Phillips curves are steeper in open than closed economies, and that output gap targeting is near-optimal as in closed economies and outperforms alternative policies ignoring cross-border or input-output linkages.