But Brattbakk ended his Premier League drought in style, sealing this rout of Kilmarnock with a clinical left-foot shot in the 88th minute, the moment which tied Celtic and Rangers at the top on points and goal difference.
In each of the last three seasons, Kilmarnock have played the role of spoiler to Celtic's championship ambitions, collecting some crucial victories, but here the Scottish Cup holders' only task was to restore some pride after losing their grip on the silverware at Ayr last week.
In a neat, ironic twist, the man Kilmarnock were relying on most was Gordon Marshall, the keeper they bought from Celtic just a month ago. Marshall's last league game was on this ground last August, a 2-0 defeat against Dunfermline which probably cost him his job at Celtic.
Marshall, though, showed after only three minutes that he still possessed the ability which once made him a Scotland international, psyching out Brattbakk after he had run clear to smother his shot. But Brattbakk gave Marshall no chance seven minutes later, when he put Celtic in front. The Norwegian,could hardly miss after Henrik Larsson beat the off-side trap to collect Jackie McNamara's pass and draw Marshall before squaring for his partner to tap into the net.
Brattbakk could have doubled his tally in the 15th minute with a splendid piece of timing when he raced clear again and waltzed round Marshall, but his shot struck a post and stayed out.
Kilmarnock gradually stemmed the tide and Jim McIntyre, making his first start in six months after knee surgery, came close with a good run down the right and a shot just over the bar. Celtic, however, went further ahead in the 36th minute and again Brattbakk did the damage from every striker's favourite distance - two yards. Larsson found Craig Burley with a quick free-kick and the former Chelsea midfielder found the unmarked Brattbakk who did the rest.
Larsson should have put the result beyond doubt three minutes after half- time when Brattbakk set him up but he tamely shot straight at Marshall. Then Larsson created an opening after 52 minutes but Brattbakk lofted the ball over Marshall only to see it strike a post, roll along the line but refuse to go in.
Celtic's keeper Jonathan Gould broke his inactivity with a fine save in the 56th minute to keep out a header by Gary Holt. But Brattbakk resumed normal service in the 70th minute with his third goal. The spadework was done by Simon Donnelly, who had replaced McNamara seven minutes earlier, breaking down the right before cutting back a perfect ball for Brattbakk to score with his right foot.Reuse content