Commons opened the scoring in the 35th minute before former Hoops forward Niall McGinn levelled in first-half stoppage time.
Georgios Samaras and McGinn both hit the woodwork as the sides swapped chances in the second half before Boerrigter, on for Teemu Pukki, prodded the ball over the line in the first minute of added time after Jamie Langfield had parried a Virgil van Dijk header.
The Dons were stunned again moments later when Commons slammed the ball in from close range to extend the leaders' unbeaten league run to 13 games.
Aberdeen have not won in the league at Parkhead since 2004 and they will perhaps feel aggrieved they did not leave Glasgow with a point, although the Hoops will have to improve their game when they face AC Milan in their crunch Champions League Group H clash at Parkhead on Tuesday night.
With that match in mind, manager Neil Lennon drafted in Samaras and Commons as winger James Forrest dropped out with a hamstring strain, with midfielder Nir Biton starting on the bench.
The Dons showed one change with Joe Shaughnessy in for former Hoops midfielder Willo Flood, who is out with a hamstring injury.
The game started at break-neck speed with the home side looking to make a quick breakthrough.
In the fifth minute, Celtic left-back Emilio Izaguirre found Scott Brown with a cross to the back post but the Celtic and Scotland skipper failed to make proper contact.
The next source of danger to the Dons came from Hoops right-back Darnell Fisher, who curled a left-footed shot in from 20 yards forcing a decent save from Langfield.
With Calvin Zola playing as a lone striker, the visitors were showing some signs of being a threat whenever they moved forward.
However, the Hoops still looked the most likely to score and in the 18th minute defender Efe Ambrose went on a mazy run through the middle which took him straight into the Dons box before he fired over.
Samaras had an effort blocked by Langfield before the Dons number one saved a Pukki header from close range after being set up by Izaguirre.
Commons' goal, though, came when Langfield punched clear an Izaguirre cross only to see it fall straight to the former Derby and Nottingham Forest player, who slammed it back in to an empty net.
The goal looked to be enough to give the home side the interval lead but the Dons drew level in time added on by referee Craig Thomson at the end of the first half.
Jonny Hayes' corner from the left was headed back into the box by Pittodrie defender Andrew Considine, with Zola beating Forster to flick the ball on and McGinn bundling it over the line from a yard out.
It had been a mostly backs-to-the-wall first half for the Dons but they trotted up the tunnel finding themselves back in the game.
There was a weak appeal for a Celtic penalty at the start of the second half when Joe Ledley went to ground under pressure from Michael Hector but referee Thomson played on.
The Wales midfielder took his frustration out on the ball moments later with a thunderous drive from 25 yards which had Langfield stretching to tip over the bar for a corner.
The corner came to nothing but Celtic were clearly playing with more urgency - at times too much urgency - as they drove forward looking to restore their lead.
As the game opened up further, Celtic midfielder Charlie Mulgrew sent Samaras through the middle of an exposed Dons defence in the 61st minute but the Greece striker slammed his shot off the post, before Langfield made a fine save from Commons' angled-drive at the expense of another corner which came to nothing.
Celtic Park braced itself for a traditional late onslaught after Amido Balde replaced Ledley in the 79th minute but it was the visitors who might have scored two minutes later when Shaughnessy headed a Wylde corner over the bar when unmarked.
In the final stages Samaras sent a header wide from eight yards and McGinn had a decent scissors-kick saved by Forster before driving a shot off the post after a mistake by Izaguirre.
But following Mulgrew's corner in the first of three minutes of added time, Boerrigter knocked the ball over the line before Commons clinched the win from close range with almost the last kick of the game after another save from Langfield, this time from Samaras, landed at his feet.
- Sports & Recreation
- Jamie Langfield
- Georgios Samaras