A shock defeat in midweek to Inverness had put pressure on Neil Lennon's side but they responded in the right manner and Brown put them ahead in first-half stoppage time with a close-range header after being set up by James Forrest.
However, it was a wonderful 25-yard drive from Commons in the 68th minute which sealed the win and took the Hoops back to within one point of SPL leaders Rangers with two games remaining.
It promises to be an exciting final week in the title race with Celtic going to Hearts on Wednesday before hosting Motherwell on Sunday, while Rangers play Dundee United at Ibrox on Tuesday before travelling down to Rugby Park on the last day.
With Georgios Samaras and Anthony Stokes suspended and midfielder Beram Kayal out for the rest of the season with a wrist injury, Hoops boss Lennon rang the changes.
In came Thomas Rogne, Ki Sung-yueng, Forrest and Daryl Murphy as Charlie Mulgrew and Shaun Maloney dropped to the bench.
Kilmarnock caretaker boss Kenny Shiels was also forced into a reshuffle with James Fowler suspended and Jamie Hamill out with hamstring injury.
Garry Hay, James Dayton and Kieran Agard came in as Willy Aubameyang dropped to the bench.
Killie, without a win in five matches, started positively with a bold three-man attack but it was Hoops midfielder Commons who had the first effort on goal in the sixth minute, his drive from 20 yards flying high over the bar.
Moments later in a swift Kilmarnock breakaway engineered by midfielder Alexei Eremenko, Dayton turned inside Celtic defender Daniel Majstorovic and fired a left-footed drive from 12 yards just past the near post.
An entertaining match warmed up further and in the 11th minute Murphy tried his luck from the edge of the box after getting the break of the ball but his low drive sped past the far post.
In the 20th minute Gary Hooper had the ball in the net after Killie keeper Cameron Bell had saved a Majstorovic header from a Commons free-kick, but the flag was up for offside.
But it was an indication that Celtic were taking a grip of proceedings and a surging run by Murphy took him into the Killie box before the former Sunderland man's cross was cut out by Bell.
Ki was booked for a foul on Eremenko on the half-hour mark as the playmaker broke clear over the halfway line to threaten the visitors' rearguard.
Killie defender Manuel Pascali joined him in the book moments later for bundling Murphy to the ground outside the box and from the resultant free-kick Commons clipped the top of the bar.
In the 33rd minute the Scotland midfielder had the ball in the net from six yards after Murphy poked the ball through to him but referee Willie Collum again blew for offside to the anger of the travelling fans.
As play swung from end to end Eremenko broke clear again but this time his poor shot was easily saved by Fraser Forster.
The game looked to be heading to the interval goalless but, seconds into the first of two added minutes, Brown headed in from close range after Forrest had headed back a Murphy cross and with that, the visitors trooped into the dressing room in a different frame of mind.
Celtic bounded out for the start of the second half and within a minute Forrest and Murphy worked a one-two at the edge of the box before the former volleyed over the bar.
Then, Forrest, clearly buoyed by his contribution to the goal, went past Hay in the Killie box only to drive into the side netting, before Ki watched his long-range attempt drift high and wide.
Celtic looked in control but in the 51st minute a moment of slackness by Majstorovic at the back allowed Agard a chance but the Killie striker's left-footed drive was blocked by the covering Rogne.
Five minutes later Kilmarnock defender Mohamadou Sissoko appeared to pull a hamstring and youngster Alex Pursehouse came on to make his debut.
In the 65th minute Maloney replaced Forrest and Mehdi Taouil came on for David Da Silva, who had been ineffective for Killie.
However, three minutes later it was all over for the hosts when Commons, almost casually, fired in a wonderful drive from 25 yards which gave Bell no chance.
The tempo of the game dropped but Celtic kept pushing forward to try to improve their goal difference - in the end to no avail, but their win took the tight title race into its final week.