Speculation about the Norwegian's future intensified after the home goalless draw against Dundee in midweek cut the Hoops' lead over Aberdeen at the top of the Ladbrokes Premiership to four points.
The increasingly disgruntled Celtic faithful had stayed away in their droves with Parkhead around a quarter full but the home side were fully focused and first half goals from Leigh Griffiths, Gary Mackay-Steven and Callum McGregor allayed any prospects of a shock.
The Championship side, who had triumphed 1-0 after extra-time when the sides met in the League Cup in 2013, escaped the second half having suffered no more damage as Celtic twice hit the woodwork with Deila hearing a round of applause at the end of the match.
Once again the Celtic boss had tinkered with his starting line-up.
Kris Commons, Stefan Johansen, McGregor and Mackay-Steven all returned while Charlie Mulgrew moved back to centre-back to replace the injured Dedryck Boyata.
The low attendance and noon kick-off did little to enhance the encounter.
Celtic's Gary Mackay-Steven (R) in action with Greenock Morton's Lee Kilday
Image credit: Reuters
Morton appeared to be settling into the match but were undone rather easily in the 14th minute when defender Thomas O'Ware was caught under a cross from Mackay-Steven, allowing Griffiths time and space to force his shot past keeper Derek Gaston for his 34th goal of the season.
The home side looked sharper than they did in midweek and Gaston had to save with his feet from Griffiths but moments later, in the 25th minute, the keeper had no chance when, from six yards, Mackay-Steven converted a Kieran Tierney pass.
Celtic keeper Craig Gordon did have to a make a good save from Stefan McCluskey but the home side were in determined mood.
In the 35th minute, after Commons had failed to get enough on a header from a Tierney cross, it was all too easy for McGregor to cruise towards the edge of the box before curling the ball past Gaston and into the corner.
There was a moment of controversy seconds before the end of the first half when Johansen was caught by Michael Miller, moments after the Morton defender had been booked for a foul on McGregor.
However, to the anger of Hoops players and fans, referee Willie Collum played on before blowing for the interval and the Celtic midfielder was helped up the tunnel, replaced for the start of the second half by striker Colin Kazim-Richards.
Patrick Roberts took over from Griffiths on the hour mark, moments later striking the base of the post with a drive from the edge of the box.
The introduction of forward Bobby Barr for Miller in the 51st minute gave Morton a boost going forward and in the 66th minute, following a corner, Gordon made a point-blank save from Declan McManus.
However, there was no danger of a fightback and minutes later Mackay-Steven thundered a shot against the underside of the bar as Celtic pressed again.
Roberts was making a good impression with his pace and trickery and he forced Gaston into a fine save with a drive but the game petered out with Celtic unable to add to their lead but more than happy to get back to winning ways.