Kenny Shiels said this was the best Celtic have played in a long time in the SPL as Kilmarnock were beaten at Rugby Park.
Following their qualification for the last 16 of the Champions League, Neil Lennon’s side can concentrate on domestic matters until February.
Captain Scott Brown scored the opening goal for the Hoops to give them the lead at the break.
Paul Heffernan had a great chance to equalise for the hosts but his shot was blocked by Charlie Mulgrew with Fraser Forster beaten.
Joe Ledley was back in the starting line up for the visitors and he made it 2-0 just after the hour mark.
A fine team goal saw substitute Georgios Samaras head in a third before Cillian Sheridan netted a consolation goal in the final minute.
When asked why the performance was so convincing, Lennon said: "I think it is was down to the fact that we are through (in the Champions League).
"The confidence is there, we are not looking a week or two down the line for the next Champions League game and maybe saving a little bit for that.
"We know the consistency in the league hasn't been totally there but away from home we have been very good, we want to replicate that at home now.
"We have opened up a gap and it's up to the other teams to win their games and keep in touch with us.
"Three points with a game in hand is a good position to be in now."