They doubled their lead seven minutes later as Rainford Kalaba broke the Senegal offside trap to round the goalkeeper and slot in.
Moussa Sow had an early chance for Senegal in the second half, but he could only hook his effort over the crossbar.
The first sign of danger from Demba Ba came just after the hour as he fired a shot narrowly wide of the Zambia goal.
Senegal pulled a goal back with 15 minutes to play as Dame Ndoye smashed a half-volley in from the angle.
Despite a frantic search for an equaliser, Senegal were met by some resolute defending as Zambia held on for the win.