The　recently　discovered　kagome　superconductors　AV3Sb5　exhibit　tantalizing　high-pressure　phase　diagrams,　in　which　a　new　domelike　superconducting　phase　emerges　under　moderate　pressure.　However,　its　origin　is　as　yet　unknown.　Here,　we　carried　out　the　high-pressure　electrical　measurements　up　to　150　GPa,　together　with　the　high-pressure　x-ray　diffraction　measurements　and　first-principles　calculations　on　CsV3Sb5.　We　find　the　new　superconducting　phase　to　be　rather　robust　and　inherently　linked　to　the　interlayer　Sb2-Sb2　interactions.　The　formation　of　Sb2-Sb2　bonds　at　high　pressure　tunes　the　system　from　two-dimensional　to　three-dimensional　and　pushes　the　pz　orbital　of　Sb2　upward　across　the　Fermi　level,　resulting　in　enhanced　density　of　states　and　increase　of　TC.　Our　work　demonstrates　that　the　dimensional　crossover　at　high　pressure　can　induce　a　topological　phase　transition　and　is　related　to　the　abnormal　high-pressure　TC　evolution.　Our　findings　should　apply　for　other　layered　materials.　©　2022　American　Physical　Society.