Stewart Downing had a good game for England at the Riverside and provided the cross that gave Carlton Cole his second goal, to put England 2-0 up just before half-time.
Cole had earlier given England the lead after 13 minutes.
The game stayed at 2-0 until Ukraine pulled one back with two minutes left. Then in injury time Marcus Bent made it 3-1 to England.
England Team:
Carson, Hunt (Hoyte 46), Richards (Harding 46), Ferdinand, Kilgallon, Milner (Bent 59), Pennant, O'Neil, Cole (Whittingham 46), Stead (Ashton 46), Downing (Reo-Coker 76).