St Johnstone striker Michael O'Halloran caused Celtic some early problems before Turkish striker Ciftci made the most of a rare start to fire home the opener from a 35th-minute corner.
The home side missed good chances to equalise before the break and were made to pay for their profligacy in front of goal when Dedryck Boyata bulleted home Celtic's second in the 49th minute.
Ciftci doubled his Celtic tally for the season as he headed home Mikel Lustig's cross in the 67th minute to move the Glasgow giants four points clear of Aberdeen with a game in hand over their nearest challengers.
Before the game, Emilio Izaguirre warmed up for the match in a T-shirt sporting an emotional message in memory of his Honduran team-mate Arnold Peralta, who was recently murdered in his homeland. The pair shared a house in Glasgow when Peralta was playing for Rangers.
Sentiment was soon put to one side, however, as St Johnstone caught Celtic napping with a flying start.
Only a fine block by Craig Gordon stopped the Saints opening the scoring after O'Halloran latched onto a through-ball from Steven MacLean to go one-on-one with the Hoops goalkeeper.
The St Johnstone striker's pace caused the Celtic defence problems and only a timely intervention from Jozo Simunovic prevented O'Halloran from racing through again.
Australian international Tom Rogic's clever play then sent Ciftci through on goal, but the striker was careless with his finish and sent his shot straight at Alan Mannus.
However, Ciftci made amends for his earlier miss by slamming in the opener.
Lustig flicked on a corner to the far post, where the Turkish striker took a touch before drilling the ball into the bottom left-hand corner of the net.
A great double save stopped St Johnstone from levelling as Gordon blocked a shot from Murray Davidson before getting down low to keep out the rebound from David Wotherspoon.
O'Halloran then evaded a last-ditch tackle from Simunovic to break into the box, but the forward misjudged his angles and curled his effort wide.
St Johnstone were left to rue their missed chances as Boyata registered his fifth goal of the season to double Celtic's advantage three minutes after the break.
The Belgian defender raced into the box to meet Callum McGregor's corner and sent a powerful header past the helpless Mannus.
Celtic made sure of the three points when Ciftci headed home his second of the match.
Rogic fed Lustig down the right and his perfectly weighted cross was sent bouncing into the turf and beyond Mannus by the Turk.