Griffiths missed much of last season after taking an extended leave of absence to deal with mental health problems and he made a strong impact upon his return as Celtic put one foot into the third round of qualifying.
Estonian side Kalju managed to frustrate its host in the early exchanges, but Kristoffer Ajer gave Celtic a deserved lead in the 36th minute and it was one-way traffic from there as Christie and Griffiths' fine strike in the final moments of the first half had the Scottish champion cruising.
Celtic appeared to ease up a little after the break, though it extended the lead just past the hour with Christie's spectacular second goal and wrapped things up with Callum McGregor's late drive.
After a somewhat slow start by Celtic, it ended Kalju's resistance with nine minutes of the first half remaining – Ajer meeting Christie's free-kick with a glancing header that went in off the crossbar.
Christie then got on the scoresheet himself soon after, converting a penalty following a blatant handball by Aleksandr Kulinits.
A few moments later, Griffths marked his return to the Celtic team in style, curling a free-kick into the top-right corner from just outside the penalty area.
Celtic, still without Kieran Tierney, remained utterly dominant despite seeming to take their foot off the gas after the interval.
Christie continued to play at full throttle, however, and he netted a brilliant fourth with 65 minutes played, bending in from 20 yards.
McGregor added the fifth 13 minutes from time, drilling into the bottom-right corner from distance, ensuring Celtic will progress to face either Cluj or Maccabi Tel Aviv in the next round, barring a second-leg capitulation in Estonia next week.