Stereocontrol of the alkyne haloboration reaction has received attention in many experimental but few theoretical studies. Here we present a detailed quantum-chemical study of mechanisms leading to Z versus E isomers of haloboration products, considering acetylene and propyne combined with BCl3, BBr3, and BI3. Calculations using B3LYP-D3, MP2, and DLPNO-CCSD(T) methods are used to study polar reactions between the alkyne and BX3 in the absence and presence of an additional halide anion whose content in the reaction mixture can be controlled experimentally. The formation of anti-haloboration products via radical mechanisms is also explored, namely, by adding BX3 to (Z)-halovinyl radical. For the anti-haloboration of propyne, the radical route is prohibited by the regiochemistry of the initiating halopropenyl radical, while the polar route is unlikely due to a competitive allene generation. In contrast, energetically accessible routes exist for both syn- and anti-bromoboration of acetylene; hence, careful control of reaction conditions is necessary to steer the stereochemical outcome. Methodologically, MP2 results correspond better to the DLPNO-CCSD(T) energies than the B3LYP-D3 results in terms of both reaction barrier heights and relative ordering of energetically close stationary points.