We investigate the low transverse momentum heavy quarkonium ( J/ψ, ϒ) productions in the forward rapidity region of pp and pA collisions at the LHC as an important probe to the transverse momentum tomography of the gluons in hadrons in the color glass condensate (CGC) framework. By implementing the Sudakov resummation consistently in the CGC formalism, we achieve an excellent agreement between the improved CGC calculations and the LHC data. We show that both the small- x and the Sudakov effects are essential for a complete description of heav...