In the four-dimensional supersymmetric standard model extended with gauge singlets the lightest Higgs boson mass, $M_H$, has an important contribution proportional to the squared of the superpotential coupling $\lambda$ of singlets to Higgs fields, $\lambda SH_1\cdot H_2$. The requirement of perturbativity up to the unification scale yields an upper bound on $M_H\sim 140$ GeV. In extensions to theories with (longitudinal) extra dimensions at the TeV where such coupling exists and massive Kaluza-Klein states fall into N=2 representations, if either of the Higgs or singlet fields live in the bulk of the extra dimensions, the $\beta$-function of $\lambda$ is suppressed due to the absence of anomalous dimension of hypermultiplets to leading order. This implies a slower running of $\lambda$ and an enhancement of its low energy value. The $M_H$ upper bound increases to values $M_H\lesssim 165$ GeV.Work supported in part by EU under TMR contract ERBFMRX-CT96-0045, and by CICYT (Spain)under contract AEN98-0816.Peer reviewed