Low-lying island nations like Indonesia are vulnerable to sea level Height EXtremes (HEXs). When compounded by marine heatwaves, HEXs have larger ecological and societal impact. Here we combine observations with model simulations, to investigate the HEXs and Compound Height-Heat Extremes (CHHEXs) along the Indian Ocean coast of Indonesia in recent decades. We find that anthropogenic sea level rise combined with decadal climate variability causes increased occurrence of HEXs during 2010–2017. Both HEXs and CHHEXs are driven by equatorial westerly and longshore northwesterly wind anomalies. For most HEXs, which occur during December-March, downwelling favorable northwest monsoon winds are enhanced but enhanced vertical mixing limits surface warming. For most CHHEXs, wind anomalies associated with a negative Indian Ocean Dipole (IOD) and co-occurring La Niña weaken the southeasterlies and cooling from coastal upwelling during May-June and November-December. Our findings emphasize the important interplay between anthropogenic warming and climate variability in affecting regional extremes.