Chambeshi’s forgettable first day came just four days after he replaced Zeddy Saileti who was fired after just 11 games in charge.
Nkana made a promising start when Shadreck Musonda put the host ahead in the 20th minute.
But Power hit back in the 41st minute through Martin Phiri who scored his first of two goals of the day.
Phiri then punished Nkana defender Donashano Malama for his poor clearance in the 46th minute to complete his brace and to ensure Power stayed unbeaten this season.
Power also extended its unbeaten derby run to four games with four wins and a draw.
Interestingly Nkana loss came a week after pacesetters Lusaka Dynamos beat them by the same margin and that result culminated in Saileti’s sacking.
Power are 1st on 20 points after the win while Nkana are 8th on 16 points following their second straight defeat.