The first measurements of dielectron production at midrapidity (ηe<0.8) in proton-proton and proton-lead collisions at sNN=5.02TeV at the LHC are presented. The dielectron cross section is measured with the ALICE detector as a function of the invariant mass mee and the pair transverse momentum pT,ee in the ranges mee<3.5 GeV/c2 and pT,ee<8 GeV/c, in both collision systems. In proton-proton collisions, the charm and beauty cross sections are determined at midrapidity from a fit to the data with two different event generators. This complements the existing dielectron measurements performed at s=7 and 13 TeV. The slope of the s dependence of the three measurements is described by FONLL calculations. The dielectron cross section measured in proton-lead collisions is in agreement, within the current precision, with the expected dielectron production without any nuclear matter effects for e+e- pairs from open heavy-flavor hadron decays. For the first time at LHC energies, the dielectron production in proton-lead and proton-proton collisions are directly compared at the same sNN via the dielectron nuclear modification factor RpPb. The measurements are compared to model calculations including cold nuclear matter effects, or additional sources of dielectrons from thermal radiation.