The midfielder was everywhere again alongside Steven Gerrard as Wayne Rooney's close-range header in the 49th minute secured a 1-0 win against the co-hosts in Donetsk.
England soaked up pressure from Ukraine in the first half and had to survive a goalline controversy in the second half - John Terry cleared from under the crossbar, but Marko Devic's effort looked over the line - but held onto their slender lead.
Jermain Defoe was an unused substitute at the Donbass Arena.
With France losing against Sweden, England topped the group, missed reigning champions Spain in the quarter-finals and will now take on Italy in the last eight in Kiev on Sunday.
Last night's matches completed the group stages and the quarter-final line-up is as follows...
Czech Republic v Portugal (Warsaw, Thursday, 7.45pm)
Germany v Greece (Gdansk, Friday, 7.45pm)
Spain v France (Donetsk, Saturday, 7.45pm)
England v Italy (Kiev, Sunday, 7.45pm)