Two-particle angular correlations are measured in high-multiplicity proton-proton collisions at s = 13 TeV by the ALICE Collaboration. The yields of particle pairs at short-(∆η ∼ 0) and long-range (1.6 < |∆η| < 1.8) in pseudorapidity are extracted on the near-side (∆φ ∼ 0). They are reported as a function of transverse momentum (p_T) in the range 1 < p_T< 4 GeV/c. Furthermore, the event-scale dependence is studied for the first time by requiring the presence of high-p_T leading particles or jets for varying p_T thresholds. The results demonstrate that the long-range “ridge” yield, possibly related to the collective behavior of the system, is present in events with high-p_T processes as well. The magnitudes of the short- and long-range yields are found to grow with the event scale. The results are compared to EPOS LHC and PYTHIA 8 calculations, with and without string-shoving interactions. It is found that while both models describe the qualitative trends in the data, calculations from EPOS LHC show a better quantitative agreement for the p_T dependency, while overestimating the event-scale dependency. [Figure not available: see fulltext.]