Adam Matthews twice set up Brown in the first half either side of gifting Niall McGinn an equaliser and Anthony Stokes put Celtic further ahead early in the second half.
Aberdeen contributed to an entertaining attacking game and Shaleum Logan soon pulled them back into it with an excellent solo goal.
But the Dons were controversially denied a penalty when Jonny Hayes went down under the challenge of Efe Ambrose and Commons took his tally for the season to 30 with a brace.
Consolation for Aberdeen came in the shape of Dundee United's draw at Inverness, which means they cannot deny the Dons a top-three finish, although Motherwell closed the gap to one point in the race for second.
The visitors came to Parkhead looking for their third consecutive win over the champions but Neil Lennon's men had scored nine goals in their previous two games and looked determined to avenge previous losses.
Aberdeen showed their willingness to get forward in an even opening quarter. Commons twice came close after getting in behind the away defence and McGinn fired just wide from 20 yards at the other end after the Dons won the ball back and moved forward quickly.
Celtic took the lead in the 24th minute. Stefan Johansen opened up play with a nutmeg on Willo Flood on the halfway line and switched play to Matthews. The right-back played the ball into the box and Brown turned to make space and fired a left-footed shot inside Jamie Langfield's near post
Matthews gifted Aberdeen an equaliser three minutes later when he failed to get enough purchase on his attempt to knock the ball back to Fraser Forster as he ran across the 18-yard line under pressure, and McGinn nipped in to round the goalkeeper and slipped the ball home.
Aberdeen lost centre-forward Adam Rooney in the 37th minute after he hurt his lower leg as he collided with Forster as they raced to meet a ball forward, despite the offside flag being raised. Scott Vernon came on.
Langfield stopped a powerful strike from Commons following a tight one-two with Stokes outside the box and Hayes fired just wide from 25 yards following a good passing move down the right.
Matthews atoned for his error in the 44th minute as he set up Brown for a second time. The Wales international crossed to pick out his captain, who again fired low into the corner with his left foot.
Griffiths looked threatening at the start of the second period but Forster had to dive to push away a powerful long-range effort from Barry Robson.
Celtic extended their lead in the 53rd minute. Stokes and Mulgrew both passed up chances to shoot after Johansen had threaded the ball into the Irishman's feet inside the box, but the ball eventually ricocheted back to the feet of the striker, who stretched to poke a shot inside the near post from 10 yards.
Again, Aberdeen struck back three minutes later when Logan hit a wonderful first goal for the club. The left-back cut inside, beat two men and let fly from almost 30 yards and the ball landed inside Forster's left-hand post.
Commons almost scored with a brilliant piece of skill when he turned a man and tried to chip Langfield, but the Dons keeper got just enough of a touch at full stretch to nudge the ball over the top corner.
Celtic had a major let-off in the 65th minute when Ambrose appeared to trip Hayes just inside the box as the winger skipped past him on the counter-attack, but referee Iain Brines waved play on to the disgust of the visitors.
Celtic went further ahead in the 69th minute when Commons stabbed the ball into the corner from 10 yards after an inside pass by Stokes.
Mulgrew and McGinn both had decent efforts well saved and Flood hit the base of the post from 20 yards as Aberdeen sought a way back.
Johansen limped off as Mikael Lustig and Beram Kayal came on for the hosts, with Griffiths also making way.
And Kayal soon set up Commons with a reverse pass for the PFA Scotland player of the year to round off the scoring with a neat finish in the 87th minute.