Striker Victor Mubanga scored a second half goal at Independence Stadium to help Konkola open a one point lead at the summit.
Mubanga registered the goal in the 50th minute of this midweek rescheduled match.
The win moves Konkola to 53 points while Kansanshi remain stuck on 52 points after 27 matches played.
Seven rounds of matches are left to play in the 2020/21 season.
Meanwhile, Kafue Celtic are third on 49 points as at Week 27.
FAZ National Division 1 – Week 27 Results
Kansanshi Dynamos 0-1 Konkola Blades
Kashikishi Warriors 1-3 Zesco Malaiti Rangers
Police College 1-1 Mufulira Wanderers
Zesco Shockers 0-0 Mpulungu Harbour
KYSA 1-2 MUZA FC
Gomes FC 0-0 Chambishi
Kafue Celtics 2-1 City of Lusaka
Livingston Pirates 0-0 Nchanga Rangers
National Assembly 0-0 Trident FC