Interstellar comet 3I/ATLAS has been approaching its 2025 October 29 perihelion while opposite the Sun from Earth, hindering ground-based optical observations over the preceding month. However, this geometry placed the comet within the fields of view of several space-based solar coronagraphs and heliospheric imagers, enabling its continued observation during its final approach toward perihelion. We report photometry from STEREO-A's SECCHI HI1 and COR2, SOHO's LASCO C3, and GOES-19's CCOR-1 instruments in 2025 September--October, which show a rapid rise in the comet's brightness scaling with heliocentric distance r as r^(-7.5+/-1.0). CCOR-1 also resolves the comet as an extended source with an apparent coma ~4' in diameter. Furthermore, LASCO color photometry shows the comet to be distinctly bluer than the Sun, consistent with gas emission contributing a substantial fraction of the visible brightness near perihelion.