A Scott McDonald double at Rugby Park, which took his tally to 15 for the season, took the champions three points clear of their Ibrox rivals and in pole position to take their fourth title in succession.
Strachan played down the advantage his side regained after losing a seven-point lead to the Govan club in recent weeks.
He said: “It’s nice as we sit here but I think everyone knows that because of the way the season is panning out, there will be twists and turns before the end.
Celtic, indeed, dominated the first half but Danny Invincibile’s volley after 36 minutes cancelled out his fellow Australian’s opener 10 minutes earlier.
However, 10 minutes from the end McDonald struck with a wonderful solo goal after waltzing through the home defence to give the Parkhead side three crucial points.
Strachan said: “I thought we started the game really well and made lots of chances but we were in shock for 10 minutes after they scored.
“Scott’s first goal was terrific as well as his second so I was pleased with him.
KILMARNOCK: Combe, Clancy, Hay, Ford, Lilley, Bryson, Pascali, Hamill, Invincibile (Taouil 86), Fernandez (Sammon 57), Kyle.
CELTIC: Boruc, Hinkel, O’Dea, Caldwell, McManus, Scott Brown, Crosas, Nakamura, McGeady, Samaras (Hutchinson 78), McDonald.
Referee: C Thomson (Scotland).