The Galactic center supermassive black hole Sagittarius A* (Sgr A*) is one of the most promising targets to study the dynamics of black hole accretion and outflow via direct imaging with very long baseline interferometry (VLBI). At 3.5 mm (86 GHz), the emission from Sgr A* is resolvable with the Global Millimeter VLBI Array (GMVA). We present the first observations of Sgr A* with the phased Atacama Large Millimeter/submillimeter Array (ALMA) joining the GMVA. Our observations achieve an angular resolution of similar to 87 mu as, improving upon previous experiments by a factor of two. We reconstruct a first image of the unscattered source structure of Sgr A* at 3.5 mm, mitigating the effects of interstellar scattering. The unscattered source has a major-axis size of 120 +/- 34 mu as (12 +/- 3.4 Schwarzschild radii) and a symmetrical morphology (axial ratio of 1.2(-0.2)(+0.3)), which is further supported by closure phases consistent with zero within 3 sigma. We show that multiple disk-dominated models of Sgr A* match our observational constraints, while the two jet-dominated models considered are constrained to small viewing angles. Our long-baseline detections to ALMA also provide new constraints on the scattering of Sgr A*, and we show that refractive scattering effects are likely to be weak for images of Sgr A* at 1.3 mm with the Event Horizon Telescope. Our results provide the most stringent constraints to date for the intrinsic morphology and refractive scattering of Sgr A*, demonstrating the exceptional contribution of ALMA to millimeter VLBI.