The CP asymmetry and branching fraction of the Cabibbo-Kobayashi-Maskawa-suppressed decay B+→J/ψπ+ are precisely measured relative to the favored decay B+→J/ψK+ using a sample of proton-proton collision data corresponding to an integrated luminosity of 5.4 fb-1 recorded at a center-of-mass energy of 13 TeV during 2016-2018. The results of the CP asymmetry difference and branching fraction ratio are ΔACPACP(B+→J/ψπ+)-ACP(B+→J/ψK+)=(1.29±0.49±0.08)×10-2, Rπ/K[B(B+→J/ψπ+)/B(B+→J/ψK+)]=(3.852±0.022±0.018)×10-2, where the first uncertainties are statistical and the second are systematic. A combination with previous LHCb results based on data collected at 7 and 8 TeV in 2011 and 2012 yields ΔACP=(1.42±0.43±0.08)×10-2 and Rπ/K=(3.846±0.018±0.018)×10-2. The combined ΔACP value deviates from zero by 3.2 standard deviations, providing the first evidence for direct CP violation in the amplitudes of beauty decays to charmonium final states.