Aims. We aim to unveil the structure of the continuum and broad-emission line (BEL) emitting regions in the gravitationally lensed quasar SDSS J1339+1310 by examining the distinct signatures of microlensing present in this system. Our study involves a comprehensive analysis of ten years (2009–2019) of photometric monitoring data and seven spectroscopic observations acquired between 2007 and 2017. Methods. This work focuses on the pronounced deformations in the BEL profiles between images A and B, alongside the chromatic changes in their adjacent continua and the striking microlensing variability observed in the r-band light curves. We employed a statistical model to quantify the distribution and impact of microlensing magnifications and utilized a Bayesian approach to estimate the dimensions of various emission regions within the quasar. To establish a baseline relatively free of microlensing effects, we used the cores of the emission lines as a reference. Results. The analysis of the r-band light curves reveals substantial microlensing variability in the rest-frame UV continuum, suggesting that image B is amplified relative to image A by a factor of up to six. This finding is corroborated by pronounced microlensing-induced distortions in all studied BEL profiles (Lyα, Si IV, C IV, C III], and Mg II), especially a prominent magnification of image B's red wing. These microlensing signals surpass those typically observed in lensed quasars, and the asymmetric line profile deformations imply an anisotropic broad-line region (BLR). We estimated the average dimensions of the BLR to be notably smaller than usual: the region emitting the blue wings measures R1/2 = 11.5 ± 1.7 light-days, while the red wings originate from a more compact area of R1/2 = 2.9 ± 0.6 light-days. From the photometric monitoring data, we inferred that the region emitting the r-band is R1/2 = 2.2 ± 0.3 light-days across. Furthermore, by assessing the gravitational redshift of the UV Fe III blend and combining it with the blend's microlensing-based size estimate, we calculated the central SMBH's mass to be MBH ∼ 2 × 108 M⊙.