We discuss the emission of high momentum lepton pairs (${p}_{T}g4$ GeV) in central Au+Au collisions at RHIC ($\sqrt{{s}_{\mathit{NN}}}=200$ GeV) and Pb+Pb collisions at the LHC ($\sqrt{{s}_{\mathit{NN}}}=5500$ GeV). Yields of dileptons produced through interactions of jets with thermal partons have been calculated, with next-to-leading order corrections through hard thermal loop (HTL) resummation. They are compared to thermal dilepton emission and the Drell-Yan process. A complete leading order treatment of jet energy loss has been included. Jet-plasma interactions are found to dominate over thermal dilepton emission for all values of the invariant mass $M$. Drell-Yan is the dominant source of high momentum lepton pairs for $Mg3$ GeV at RHIC, after the background from heavy quark decays is subtracted. At LHC, the range $Ml7$ GeV is dominated by jet-plasma interactions. Effects from jet energy loss on jet-plasma interactions turn out to be weak, but non-negligible, reducing the yield of low-mass dileptons by about $30%$.