Glennon came up for a late corner to drive the ball high into the net for a share of the points after County looked to have won it with a David Winters penalty.
Saints full-back Jamie Winter escaped a booking after taking out Kevin McKinlay in full flight in the first minute.
The visitors were not holding back in the tackle and Martin Hardie did get his name in referee's Steve Conroy's book for a heavy tackle on John Rankin.
County almost took the lead in the 15th minute when Don Cowie's cross from the right was just missed by Sean Higgins in front of goal, then Rankin fired in a shot from the edge of the bow which Glennon managed to smother.
The home side kept up the pressure and after Glennon blocked Cowie's angled drive, Kevin Rutkiewicz got in the way of a Higgins effort.
In Saints' first real attack of the game in the 20th minute Kevin James headed straight into the arms of County keeper Stuart Garden.
James was involved again a couple of minutes later when Saints took the lead when the big midfielder's header was redirected high into the net by County captain Jim Lauchlan.
Garden injured himself in attempting to keep the ball out of the net and after a four-minute delay he was replaced by teenage keeper Joe Malin.
It was tough on County who dominated the early stages but lacked the killer touch in front of goal.
The tackles kept flying in and Gary McSwegan was yellow carded for a crude tackle on Saints playmaker Darren Sheridan.
Rutkiewicz was booked a couple of minutes later for dissent as the game threatened to get out of hand.
County came close again before half time when Rankin tried to pass the ball into the net but the ball flew past Glennon's right-hand post.
Saints started the second half well and Paul Sheerin carved out an opening for himself but sliced his shot well wide of target.
The County goal had a let off in the 55th minute, when a goalbound effort from Jason Scotland was deflected over the top by David Cowan.
Saints had the ball in the next a minute later when a James knock-down was headed home by Rutkiewicz, but referee Conroy spotted an infringement inside the box and the goal was chalked off.
But County got themselves back into the match when they won their fifth corner of the game in the 70th minute. Cowie swung the ball over and Higgins scrambled the ball over the line from close range.
Rutkiewicz had another effort disallowed five minutes later when he was ruled offside.
County restored their lead in the 83rd minute when Sean Webb was fouled inside the area and Winters netted from the spot.
In a dramatic finish to the game Saints keeper Glennon came up for a corner kick in the 88th minute and when the ball fell to him 10 yards out he flashed the ball high into the net.