Young-Pyo Lee also returned and scored an excellent goal to open the scoring after Jamie O'Hara had played the South Korean in on goal.
Another good team effort produced Tottenham's second goal - Chris Riley drilled a cross into the danger area before Andy Barcham finished with aplomb.
O'Hara was unfortunate not to extend the lead, Aaron Lennon also had a couple of opportunities but it wasn't to be the tricky winger's day.
Martin Jol: "Aaron Lennon was supposed to play 60 minutes, but he was enjoying himself and looked fine so he played the whole game. Young-Pyo Lee came back on Monday and has now scored his first goal for the club, so that was good. Didier arrived on the Monday so to play (only) 45 minutes on Saturday was probably a good thing."
Development Coach Clive Allen: "I thought he (Zokora) was excellent, the way he conducted himself and went about the job was first class. People were bouncing off him."
Cambridge City 0 Tottenham Hotspur XI 2 (Y-P Lee 38, Barcham 60)
Tommy Forecast
Chris Riley
Young-Pyo Lee (Charlie Daniels 46)
Stuart Lewis
Rodrigo Defendi (Joe Martin 60)
Aaron Lennon
Didier Zokora (Jamie Davis 46, David Hutton 65)
Jamie O'Hara
Charlie Lee
Simon Dawkins
Andy Barcham
Substitutes not used: Richard Stroud, Gregory Lake