Pedestrian Celtic came back from behind as Alan Thompson grabbed a double to secure victory over Scottish Premier League newcomers Falkirk in Glasgow.
The visitors shocked their hosts by taking a first-half lead when Darryl Duffy slotted home a penalty after Mo Camara fouled Steven Thomson.
But John Hartson headed home a Shensuke Nakamura cross after the break.
Thompson flashed a 20-yard volley past goalkeeper Matt Glennon and added a third with a fine free-kick.
Both sides were unchanged after Celtic playmaker Nakamura passed a late fitness test and Bobo Balde failed to engineer a move to Marseille.
Falkirk suffered an 8-1 cup hammering at Celtic Park last season.
But the First Division champions adopted a more defensive philosophy against a Celtic side hoping to continue their recent improved form.
Glennon had to fling himself to his right to tip Paul Telfer's dipping effort over the top early on.
Yet Celtic struggled to find their recent fluency, despite some flashes of skill from Nakamura.
And the visitors were presented with the perfect chance to grab a shock lead in the 39th minute when Thomson went down under the challenge of Camara.
Scotland Under-21 international Duffy stepped up to the spot and coolly send Artur Boruc the wrong way.
Celtic responded immediately after the break when Hartson rose to head home a Nakamura cross.
Duffy was given a chance to restore the lead when Craig McPherson found the former Rangers youth unmarked in the box, but the striker delayed his shot and the chance was lost.
Thompson was having a disappointing day in midfield and appeared poised to be replaced with Craig Beattie.
But, just as the young striker was preparing to come on, Hartson knocked the ball into the path of the Englishman, who hit the ball into the net from just outside the penalty box.
Thompson added a second with a fine, curling free-kick in stoppage time to ease any nerves and put a better gloss on a fairly unimpressive performance by the title hopefuls.
Celtic: Boruc, Telfer, Balde, McManus, Camara, Petrov, Lennon, Thompson, Nakamura (Beattie 80), Hartson, Zurawski (Maloney 61).
Subs Not Used: Marshall, Aliadiere, McGeady, Wallace, Virgo.
Goals: Hartson 49, Thompson 75, 90.
Falkirk: Glennon, Lawrie, Ireland, McPherson (Andy Thomson 85), Lima, O'Neil (O Donnell 79), Latapy, Steven Thomson, Rodrigues, Duffy, McBreen (Gow 65).
Subs Not Used: Hill, MacKenzie, Milne, McSween.
Booked: Lima, McBreen, Andy Thomson.
Goal: Duffy 39 pen.
Ref: A Freeland