The Greens took an eighth-minute lead through Zak Joseph, but Jay Gasson got the home side back on level terms midway through the second half.
And it looked like honours would finish even until Hendon were awarded a late penalty, when substitute Cole was fouled in the box by Police keeper Luke Williams.
Cole picked himself up to take the spot-kick and, although Williams saved it, the Hendon player reacted quickest to tuck home the rebound and give Greens boss Gary McCann a win on his 700th match in charge of the club.
A first away win of the season leaves Hendon in fourth place ahead of their trip to Dulwich Hamlet on Tuesday night.