The bulk of basaltic magmatism on the Moon occurred from 3.9 to 3.1 billion years ago on the ancient lunar mare plains. There is evidence for basaltic volcanism as recently as 2.9 billion years ago from crystallization ages and a billion years ago from stratigraphy. An enigmatic surface formation named Ina (18.65° N, 5.30° E) may represent much younger mare volcanism, but age estimates are poorly constrained. Here we investigate 70 small topographic anomalies, termed irregular mare patches (100-5,000 m maximum dimension), on the lunar nearside with irregular morphologies and textures similar to Ina, using Lunar Reconnaissance Orbiter narrow angle camera images, digital terrain models and wide angle camera colour ratios. The irregular mare patches exhibit sharp, metre-scale morphology with relatively few superposed impact craters larger than ten metres in diameter. Crater distributions from the three largest irregular mare patches imply ages younger than 100 million years, based on chronology models of the lunar surface. The morphology of the features is also consistent with small basaltic eruptions that occurred significantly after the established cessation of lunar mare basaltic volcanism. Such late-stage eruptions suggest a long decline of lunar volcanism and constrain models of the Moon's thermal evolution.