Oscillations have long been observed in the sunspot umbral chromosphere and transition region, connected to global p-mode oscillations. These p-modes are thought to undergo mode conversion to slow magnetoacoustic waves in regions of strong magnetic field. More recently, propagating oscillations have also been observed in solar coronal loops. Using new spectroscopic imaging data at transition-region temperatures, combined with coronal imaging, we present direct observations of the propagation of these slow magnetoacoustic p-modes through the transition region and into the solar corona, along the magnetic field. The waves are observed as oscillations in the chromosphere/transition region and propagations in the corona due to the emission scale height of the different temperature lines combined with the magnetic field geometry.