Nigerian striker Godwin Ndubuisi helped the home side end the first half one-nil up after he followed in Abdullah Saied’s of-the-bar effort into the net on 12 minutes.
After the break, Abd-Rabou scored a quickfire double in the 55th and 57th minutes, courtesy of a deflected freekick and a long-range strike into the bottom corner.
Police pulled one back four minutes later through Salah Ashour, who beat Mohamed Fathi on a second attempt from point-blank range.
But the on-fire Abd-Rabou put the scoreline beyond doubt with a superb freekick from over 30 yards out on 68 minutes.
Ismaili revive their title hopes by gaining the 42nd point to become four points behind leaders Zamalek, who host MCDR later on Thursday.
Police’s title hopes are dashed as they remain fifth on 36 points.
Bottom victories
Elsewhere, Arab Contractors and Wadi Degla boosted their survival hopes with victories over Smouha and Gouna respectively.
In Alexandria, home side Smouha were undone by two goals from Contractors' rising star Mohamed Salah.
In another bottom-of-the-table clash, Ashour Al-Taqui scored a brace to help Degla beat Gouna 3-1 in Cairo.