Cox rose to head home Barry Cogan's injury-time corner to prevent Leeds from setting a new post war record of eight successive league wins.
Dennis Wise's men looked to have grabbed an early opening on 15 minutes but Tresor Kandol's tidy finish from ten yards was ruled out by the offside flag.
Gillingham, who made six changes, had chances themselves including a fierce Andrew Crofts volley that Casper Ankergren could only parry.
But on 28 minutes the visitors edged in front when Matt Heath headed Jonathon Douglas' free-kick across goal and Seb Carole found the net with a far post header via a slight deflection.
The visitors were stunned shortly before the interval though when Kandol, already on a booking for dissent, was ordered off for sarcastically applauding the referee following a foul against him.
Leeds were infuriated further shortly before the hour when Jermaine Beckford was shown two yellow cards within minutes - the first for dissent and the second for a foul on Sean Clohessy.
Gillingham threw on an extra striker in Gary Mulligan but their finishing was woeful as they attempted to wear down a tiring Leeds defence.
Crofts headed a decent chance over from a corner before Cox blazed another effort over the bar as the clock ticked down.
Leeds kept everyone behind the ball in their frantic attempt to preserve their lead.
The plan appeared to be working until Cox pounced from Cogan's corner to send the home fans into raptures just moments after the fourth official had implicated five minutes of stoppage time.
The controversial referee required a police escort from the field as furious Leeds fans vented their anger at the official at full-time.