The cooperative effect of Rashba spin-orbit coupling (SOC) and Coulomb attraction in stabilizing topological spin-triplet excitonic condensates (ECs) in two-dimensional electron-hole systems in external magnetic field is investigated by using an unrestricted Hartree-Fock approach combined with the random-phase approximation. At weak electron-hole Coulomb interaction, the intraband Rashba SOC induces spin-momentum locking and topological semimetal behavior, while stronger interaction stabilizes spin-triplet ECs. Increasing the valence-band SOC drives a transition from a topologically trivial EC with coexisting spin-up and spin-down components to a topological spin-up EC only with quantized Chern number $C=2$. The dynamical excitonic susceptibility reveals a soft spin-up triplet mode acting as the precursor of the condensate. These results establish a microscopic mechanism for Rashba SOC-induced topological ECs and suggest realistic situations for their realization in noncentrosymmetric Janus transition-metal dichalcogenides and twisted van der Waals heterostructures.

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• Excitons
• Spin-orbit coupling
• Topological phase transition
• Zeeman effect
• Bose-Einstein condensates
• Topological materials
• Transition metal dichalcogenides
• Two-dimensional electron system
• Mean field theory
• Random phase approximation