The emplacement mechanisms of rhyolitic lava flows are enigmatic and, despite high lava viscosities and low inferred effusion rates, can result in remarkably, laterally extensive (>30 km) flow fields. Here we present the first observations of an active, extensive rhyolitic lava flow field from the 2011-2012 eruption at Cordón Caulle, Chile. We combine high-resolution four-dimensional flow front models, created using automated photo reconstruction techniques, with sequential satellite imagery. Late-stage evolution greatly extended the compound lava flow field, with localized extrusion from stalled, ~35 m-thick flow margins creating >80 breakout lobes. In January 2013, flow front advance continued ~3.6 km from the vent, despite detectable lava supply ceasing 6-8 months earlier. This illustrates how efficient thermal insulation by the lava carapace promotes prolonged within-flow horizontal lava transport, boosting the extent of the flow. The unexpected similarities with compound basaltic lava flow fields point towards a unifying model of lava emplacement.