كتب : Hatem Maher
Ivorian striker Violete Armand put Police ahead in the 31st minute to take his tally to three league goals.
He exchanged passes with Reda Al-Azab before finding the net with a precise shot from the edge of the area.
Veteran left-back Tarek Al-Sayed, who joined Tersana from Telecom Egypt in January, scored his first goal for the Hammers to equalize on the stroke of halftime.
He latched onto a delicate chipped pass from fellow new signing Amr Samaka to send a half-volley beyond the reach of Police keeper Mohamed Khalaf.
Substitute Hassan Mostafa was introduced in the 76th minute and he made an immediate impact, setting-up Nigerian striker Minusu Buba for the precious winner.
Mostafa, on loan from Ahli, released Buba with a deft pass and the latter made no mistake from close range to give Police all three points.
The win helped Talaat Youssef's side move to tenth place in the league table with 20 points.
Tersana, who haven't won any game since thrashing Olympic 4-0 on November seventh, lie second from bottom on 13 points, five adrift of the safety zone.