The Liverpool striker netted from close range in the 79th minute after being set up by Swansea City forward Tammy Abraham. It turned out to be a crucial goal after Scotland had just pulled one back after they found themselves 2-0 down.
Solanke played the opening 84 minutes while fellow Reds Joe Gomez and Trent Alexander-Arnold lasted the full distance.
Gomez captained Aidy Boothroyd's side and almost added a fourth goal but was denied by a brilliant save from former Liverpool Academy goalkeeper Ryan Fulton.
Abraham and Josh Onomah were also on the mark for England U21s.