The bankers opened the scoring in the 13th minute courtesy of Simon Abuko before Dennis Ng'ang'a sealed the win with a perfect free-kick in the 78th minute.
The John Kamau coached side is now third on the log with 46 points, five behind leaders Ushuru, who brushed Green Commandos 3-0.
A Titti Olesuh brace was all Kangemi All Stars needed to brush aside Kenya Police in another NSL match staged at Camp Toyoyo.
The Ghanaian, who was deployed in an unfamiliar right back position, was at the end of a parried ball in the 35th minute, before cheekily guiding the ball home from a free-kick in the 55th minute to hand his side maximum points.
Western Stima maintained their position on the log after defeating visiting St Josephs Youth 2-1. Samuel Odhiambo gave his side the lead in the 41st minute from the penalty spot before John Likhuwa leveled matters seven minutes later.
Fredrick Nyarombo hit the winner sixteen minutes after the restart to take the power men's tally of the season to 49 points.
In another match played on Wednesday, Erick Simiyu, Peter Mwangi, Sande Katumba and Abdala Mango were on target as Nairobi City Stars bounced back from their weekend defeat to beat Isibania 4-0.
Full Results: Kisumu All-Stars 2-1 Talanta, Bidco United 2-0 Nakuru All-Stars, Nairobi City Stars 4-0 Isibania, Kibera Black Stars 0-2 KCB, Kangemi All-Stars 2-0 Kenya Police, GFE 105 1-1 Administration Police, Coast Stima 1-1 Modern Coast Rangers, Joseph’s Youth 1-2 Western Stima and Green Commandos 0-3 Ushuru.