At the other end Momo Sissoko, being watched by his parent club Udinese, made a poor clearance to allow Daryl Murphy a strike at goal, which the Celtic forward drilled just wide from the edge of the box.
Celtic had the ball in the net on 19 minutes, but Gary Hooper was offside as he reacted to prod in Daniel Majstorovic's header, which Cammy Bell had saved.
With Celtic toiling to cut open the home defence Commons struck a couple of efforts over from distance.
But the midfielder came closer after the half-hour mark, shaving the crossbar with a 25-yard free-kick.
And
he was again denied by the assistant referee's flag,
having poked the ball into Bell's net when the ball
broke to him in an offside position.
Eremenko, again looking composed in possession in Kilmarnock's midfield, tried his luck from outside the box, but failed to trouble Forster.
But Celtic took the lead in first-half stoppage time through their captain Brown. (Right).
Murphy hung a deep cross to the back post, James Forrest headed back across goal, and Brown dived to head the ball in from six yards.
The goal seemed to relax Celtic, who started brightly after the break, with Forrest slamming a shot against the side netting.
But Majstorovic had his defensive partner Thomas Rogne to thank for a saving tackle on Kieran Agard after the Swede was caught on the ball on the edge of Celtic's box.
Celtic eventually got the second goal they craved on 68 minutes, with Commons yet again the scorer.
The Scotland winger took a cross-field pass from Brown and, having watched earlier efforts drift off target, found the top corner of the net with a thunderous shot from 25 yards.
Kilmarnock, who have won many plaudits for their play over the course of the season, looked lacklustre in the closing stages and Celtic ended up comfortable winners.
Sandy's Match Pic's are HERE
