Ahmed Duiedar's early penalty gave Police the lead but Ismaili skipper Mohamed Soliman 'Hommos' leveled the score in the 24th minute.
A brilliant strike by Mohab Saied put Ismaili in front eight minutes after the restart but Armand shattered the Dervishes' hopes of claiming all three points just before the final whistle.
Both sides played with ten men for long periods. Ismaili had defender Moatassem Salem dismissed in the first half while Police's Essam Abdul-Aati was sent off moments before the break.
Ismaili spurned the chance to narrow the gap with leaders Ahli to just one point.
They lie second in the table with 45 points, three behind holders Ahli, who still have a game in hand and look close to winning a fifth consecutive title.
Surprise Lead
Police took a surprise lead after seven minutes when Duiedar converted a penalty after sweeper Ibrahim Yehia tripped Abdul-Aati inside the area.
The hosts could have doubled their advantage shortly after, thanks to Ismaili's slack defending.
Midfielder Hassan Mostafa headed wide with the goal at his mercy after a pinpoint cross picked him out unmarked at the far post.
Yehia was caught napping more than once as Police launched a wave of attacks.
Ismaili sorely missed the presence of controversial defender Ibrahim Saied, who unilaterally decided to leave the club after a row over his wages.
Lone striker Mohamed Mohsen Abou-Greisha was isolated upfront but Ismaili still managed to restore parity on 24 minutes.
Ahmed Samir Farag's cross from a free kick found Hommos, who rose unmarked to head home.
Ismaili's hopes of securing a third successive victory received a blow when Salem received a straight red card for elbowing an opponent.
But they were lucky to see numbers evened up just before halftime after Abdul-Aati received his marching orders for a second bookable offense.
Wasteful
A successful counter attack saw Ismaili score the second in a superb fashion on 53 minutes.
A flowing move ended up in Police's net when talented midfielder Saied touched the ball with his right foot before using his left to fire a powerful volley that left Mohamed Khalaf with no chance.
Police pushed forward to search for the equalizer and consequently left huge gaps at the back.
Ismaili should have put the result beyond doubt on numerous occasions but careless finishing cost them a much-needed win.
Armand ghosted behind Ismaili's defense to latch onto a long ball and send a low shot beyond the desperate hands of keeper Mohamed Fathi five minutes into the additional time.