Driver had two good shots saved, put in a number of crosses and took the corners for the Tyneside club all under the watchful eyes of City Chairman Ray Ranson and manager City Coleman.
A Derek Riordan penalty in the 78th minute, decided the match.
City are going to need to bid at least £2m if they are to sign the winger who has said that European football would be a big incentative for him to stay at the Edinburgh based club.