Celtic began their defence of the Scottish Cup huffing and puffing before eventually dismissing Falkirk 3-0 at Parkhead.
The Glasgow club have been in talks this week with former Bournemouth boss Eddie Howe about the vacant managerial post.
In the meantime, interim boss John Kennedy watched the Hoops put the much-changed League One leaders under relentless pressure in their third-round tie.
But they had to wait until the 56th minute to take the lead through a deflected drive from James Forrest, who was making his first start in six months.
Midfielder Ryan Christie doubled the lead two minutes later and a more relaxed home side added another goal from substitute Mohamed Elyounoussi in the 79th minute to put a sheen on the scoreline.
After assessing the Hoops squad after the international break, Kennedy brought back striker Leigh Griffiths for his first start since January 30, with Forrest in the line-up for the first time since a Europa League tie against Riga last September before he had ankle surgery.
Tom Rogic came back into midfield with Callum McGregor, Elyounoussi and Odsonne Edouard dropping to the bench, while Falkirk management duo David McCracken and Lee Miller made eight changes to the side that drew with Dumbarton in their last league match.
Inevitably, Celtic took control of the ball from the first whistle and penned back the spirited visitors.
However, Falkirk goalkeeper Robbie Mutch was not really called upon until the 10th minute when he pushed a drive from Hoops midfielder David Turnbull past the post for a corner, from which Griffiths missed the target from 14 yards.
The visitors had to work flat out to contain Celtic.
Christie sent two efforts sailing over the crossbar and a penalty claim for Lewis Neilson's tackle on Griffiths inside the penalty area was ignored by referee John Beaton before Mutch saved a decent strike by Diego Laxalt.
Celtic's attacks continued in waves but the goal refused to come.
Turnbull skimmed the bar with the curled free-kick, Kristoffer Ajer drove into the Falkirk box before firing wide, the half ending with Forrest redirecting a header over from eight yards.
The second half continued along the same lines.
Celtic eventually broke the deadlock when Forrest took a pass from Rogic, turned back inside on to his right and fired in a drive that clipped Kyle McClelland before it sped past beat Mutch.
Two minutes later Christie's low drive from 22 yards beat the Falkirk keeper at his near post to end any sense of jeopardy.
Albian Ajeti replaced Griffiths before Forrest missed the target after Mutch had parried a Turnbull drive to his feet.
Both sides made more replacements and Elyounoussi, on for Forrest five minutes earlier, took a Jonjoe Kenny pass and dinked the ball over Mutch from six yards.
Falkirk were drained. In the 86th minute Ajeti almost made it four with an angled drive which escaped the far post before Mutch made a fine save from skipper Scott Brown's powerful drive after he ran in behind an exhausted visiting defence.
