Clinton Kanunga had given the service men a 1-0 lead in the 14th minute before Patillah Omoto restored parity moments before the break as both sides went to halftime tied at 1-1.
In the final half, Miheso’s quickfire double in the extra time earned Police all three points.
Another newly-promoted side Talanta bagged their fourth win of the season after defeating Bidco United 2-1.
The win propelled Talanta to third in the standings with 15 points, two behind leaders Homeboyz.
At the same time, struggling Nzoia Sugar managed to end their two match losing streak as they grabbed a precious point against Nairobi City Stars following a barren midweek league match played at Ruaraka Grounds.
Before the match, pressure was heavy on the sugar millers’ shoulders as they were yet to record any win in the opening seven games where they lost five games and drew two, leaving them second bottom on the log.
In the last match of the day, Humphrey Ochieng scored an 80th minute winner as Sofapaka defeated Wazito 2-1 at Wundanyi Stadium.
Lawrence Juma had given Batoto ba Mungu the lead in the 44th minute before Ellie Asieche leveled the scores 10 minutes after the restart.
With the match heading for a tie, Ochieng had the last laugh as his goal 10 minutes from time handed Sofapaka their fourth win of the campaign.
Wednesday Results
Nairobi City Stars 0-0 Nzoia Sugar
Kariobangi Sharks 1-3 Kenya Police
Kakamega Homeboyz 2-2 Mathare United
Sofapaka 2-1 Wazito
Talanta 2-1 Bidco United
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