There were four minutes gone in the second half when Hoops defender Mikael Lustig fouled Mark Corcoran 20 yards from goal and Parkhead goalkeeper Fraser Forster had no chance when Staggies skipper Richard Brittain fired the free-kick high past him and into the net.
It looked like the Highland side would hold on for their first league win over the Glasgow giants but, in the third minute of added time, Commons pounced to tap the ball into the net from close range after County keeper Michael Fraser had spilled a shot from Hoops substitute Tony Watt, who had replaced Lustig.
The home side, who extended their unbeaten run to 37 games, might feel harshly done by and Celtic manager Neil Lennon celebrated the leveller with some gusto, as he now turns his attention to the first leg of their Champions League play-off against Helsingborg in Sweden on Tuesday night.
Elsewhere, Jamie Murphy struck twice as Motherwell claimed their first three points of the season with a 2-1 victory over Kilmarnock at Rugby Park.
Murphy opened the scoring after 11 minutes when he drove at the home defence and slotted the ball beyond Cammy Bell.
Gary Harkins levelled on the half-hour, but within five minutes Murphy was racing on to Higdon's excellent through-ball before rounding Bell and rolling the ball into the net.
Pat Fenlon's new-look Hibernian also claimed their first win of the SPL season at St Mirren.
A goal in either half from Leigh Griffiths gave them a two-goal lead, but the Edinburgh side had to withstand a fightback from Saints, who couldn't add to Steven Thompson's goal.
However, the hosts were perhaps made to rue their penalty miss, with Paul McGowan's first-half spot-kick saved by Hibernian keeper Ben Williams.
Aberdeen completed a trio getting their first win of the new season after dominating St Johnstone in a 2-1 victory.
Issac Osbourne and Jonny Hayes provided the goals but the score does not come close to describing the visitors' superiority, particularly in a second half where Aberdeen controlled the play and created numerous chances.
Nigel Hasselbaink added a late consolation for the hosts, but the defeat from the season home opener leaves St Johnstone with only a point from their first three SPL games.
Inverness Caledonian Thistle struck with the last kick of the game as the Highlanders claimed a dramatic 2-2 draw in a controversial encounter against Hearts.
Teenager Conor Pepper rescued a draw after Terry Butcher's men appeared dead and buried at the break - two goals down and a man down following a tempestuous first period.
Arvydas Novikovas had given the hosts the lead on 15 minutes, curling past Ryan Esson, before John Sutton doubled Hearts' lead after a debatable penalty award.
Richie Foran was shown a red card on the stroke of half-time, prompting the fury of Butcher, but Caley were handed a lifeline with a penalty of their own, Andrew Shinnie netting. Pepper then sparked wild celebrations among the visitors deep into injury time.