Sunday's match at McDiarmid Park was still goalless when, with just nine minutes remaining, Christie curled in a free-kick from out wide that appeared to go straight into Zander Clark's net, although Christopher Jullien also claimed the goal.
Celtic manager Neil Lennon had demanded an "angry reaction" from his side following their midweek Europa League round of 32 exit at the hands of Danish side FC Copenhagen, but the Hoops were frustrated for much of the match by a resolute St Johnstone.
But they did just enough in the end to record a 34th successive win in a domestic cup competition.
The Hoops, who have won the last three Scottish Cup finals and are eyeing a ninth straight league title, will be favourites to extend that sequence to 36 wins given arch-rivals Rangers' quarter-finals loss to Hearts on Saturday.
Celtic will face Aberdeen in the last four, with the other semi-final drawn Sunday an Edinburgh derby between Hearts and Hibernian.
Both ties will be played on the weekend of April 11-12.