Herbert Okoth had put AP on the front foot early in the match, but Mutua would restore parity to see the first half ended 1-1 in the battle of the law enforces.
Mutua completed a brace after Douglas Museve put AP in the lead upon resumption in an entertaining draw.
Wazito, meanwhile, became the only side to have maintained a perfect start to their season following their 1-0 win over Kibera Black Stars at Camp Toyoyo.
Kennedy Ayako scored the lone goal as Wazito nicked a fourth win in four matches.
Midweek Results: Green Commandos 0-3 Ushuru (Bukhungu Stadium), Thika United 1-1 Fortune Sacco (Thika Stadium), Bidco United 1-1 Nairobi City Stars (Thika Stadium), Shabana 0-0 Migori Youth (Gusii Stadium), Eldoret Youth 2-0 Kangemi All-Stars (Walkover), Nairobi Stima 4-0 Modern Coast Rangers (Karuturi Grounds), Administration Police 2-2 Kenya Police (Camp Toyoyo), FC Talanta 1-1 Coast Stima (Camp Toyoyo), Wazito 1-0 Kibera Black Stars (Camp Toyoyo), Kisumu All Stars 0-0 St. Joseph’s Youth (Moi Stadium Kisumu)