Investigating the overall brightness of planets (and moons) provides insights into their envelopes and energy budgets1–4. Phase curves (a representation of the overall brightness versus the Sun–object–observer phase angle) for Titan have been published over a limited range of phase angles and spectral passbands5,6. Such information has been key to the study of the stratification, microphysics and aggregate nature of Titan’s atmospheric haze7,8 and has complemented the spatially resolved observations showing that the haze scatters efficiently in the forward direction7,9. Here, we present Cassini Imaging Science Subsystem whole-disk brightness measurements of Titan from ultraviolet to near-infrared wavelengths. The observations show that Titan’s twilight (loosely defined as the view at phase angles ≳150°) outshines its daylight at various wavelengths. From the match between measurements and models, we show that at even larger phase angles, the back-illuminated moon will appear much brighter than when fully illuminated. This behaviour is unique in our Solar System to Titan and is caused by its extended atmosphere and the efficient forward scattering of sunlight by its atmospheric haze. We infer a solar energy deposition rate (for a solar constant of 14.9 W m−2) of (2.84 ± 0.11) × 1014 W, consistent to within one to two standard deviations with Titan’s time-varying thermal emission from 2007 to 201310,11. We propose that a forward scattering signature may also occur at large phase angles in the brightness of exoplanets with extended hazy atmospheres and that this signature has a valuable diagnostic potential for atmospheric characterization.