Production cross sections of Image 1, Image 2, and Image 3 states decaying into Image 4 in proton-lead (<math altimg="si2.svg"><mi mathvariant="normal">p</mi><mrow><mi mathvariant="normal">Pb</mi></mrow></math>) collisions are reported using data collected by the CMS experiment at <math altimg="si3.svg"><msqrt><mrow><msub><mrow><mi>s</mi></mrow><mrow><msub><mrow/><mrow><mi mathvariant="normal">NN</mi></mrow></msub></mrow></msub></mrow></msqrt><mo linebreak="goodbreak" linebreakstyle="after">=</mo><mn>5.02</mn><mspace width="0.2em"/><mtext>TeV</mtext></math>. A comparison is made with corresponding cross sections obtained with <math altimg="si4.svg"><mi mathvariant="normal">p</mi><mi mathvariant="normal">p</mi></math> data measured at the same collision energy and scaled by the Pb nucleus mass number. The nuclear modification factor for Image 1 is found to be Image 5. Similar results for the excited states indicate a sequential suppression pattern, such that Image 6. The suppression of all states is much less pronounced in <math altimg="si2.svg"><mi mathvariant="normal">p</mi><mrow><mi mathvariant="normal">Pb</mi></mrow></math> than in PbPb collisions, and independent of transverse momentum Image 7 and center-of-mass rapidity Image 8 of the individual Image 9 state in the studied range Image 10 and Image 11. Models that incorporate final-state effects of bottomonia in pPb collisions are in better agreement with the data than those which only assume initial-state modifications.