Veteran Sylvester Louis hit an unbeaten 72 and stand-in captain Stanton Proverbs a crucial 60 as they steered the team to full points with an unbroken seventh-wicket partnership of 145.
Resuming on 77 for six yesterday and needing an additional 83 runs with four wickets intact, Police steadily loosened Pickwick's grip on the game with some positive batting.
The lawmen, who were dismissed for a first innings 21 on Sunday, clinched victory just after 3 p.m., closing on 160 for six.
Louis, who gave the Police batsmen heart with 34 not out on a difficult second day, survived a dropped chance in yesterday's first over, bowled by Wayne Yarde, but made his team's intentions clear as he took 10 runs off the over.
Proverbs would not be outdone and also stroked the ball confidently, picking up runs all around the wicket as the bowlers were unable to break through.
As Police were coasting home with little bother, their victory was postponed for just over an hour when showers intervened with the score on 157 for six.
This forced the umpires to call an early tea and when play resumed at 3 p.m., Louis and Proverbs took singles off the second, third and sixth balls of Wren Miller's eighth over to push Police back to the top of the standings.
Louis, a veteran seamer who is also enjoying an impressive run with the bat this season, sealed the victory as he turned Miller to square-leg.
``I was praying for conditions to improve because I always thought we had a chance.
``We are fighters ... and we will be fighting against BET in our next match,'' said Louis who plans to retire at season's end.
The final twist in this rain-affected game turned out to be a bitter result for Pickwick, following the performance of Yarde on Sunday where he took six wickets in the Police first innings and four in the second.
Pickwick captain Mike Matthews said they were pressing to prevent the match from entering the third day but were let down by spilled chances.