Kris Commons opened the scoring, blasting home a rebound before controversy ensued at the other end as penalty appeals were waved away when Scott Brown barged over Ryan Dow in the box.
United were reduced to 10 men when Sean Dillon was sent off for a reckless lunge in on Emilio Izaguirre before substitute James Forrest scored from the edge of the box and then missed a penalty.
It keeps the Hoops firmly on course for the treble – the Holy Grail for Norwegian boss Deila who has repeatedly spoke of his desire to land a domestic clean sweep.
United remain an obstacle in Celtic’s quest with the Scottish Cup quarter-final replay on Wednesday to come and further meetings in the Scottish Premiership.
But on this evidence it suggests it’s a hurdle the Hoops can overcome.
Celtic boss Deila spoke of his delight after the game and made light of the incident involving Scott Brown in midweek: “We have talked about this many times. It is a dream. It is so tough to do it but it is possible. The dream is still alive and I happy.
“Now we have one trophy and Wednesday we have to be back again to make another cup, so it is going quick in this job.
“We should enjoy this moment but there is not going to be any nightlife.”
Deila added that it wasn’t a big issue that the Celtic captain was pictured out during the week of the Cup final.
“It’s not a big case. He was home at 10:30 it looks like he was home at six in the morning. He was drinking he had the day off. I have no rules about that.
“I said the players have to be fit and Scott Brown is the fittest player we have but we have a representation to take care of we weren’t proud of the pictures and things that appeared in the newspaper.
“We have to learn from this. When you are playing for Celtic everybody is chasing you don’t get personal time so you have to always know what you are doing.”
Meanwhile, Jackie McNamara lamented the decision which saw Dillon off the park for eight first-half minutes when Celtic scored.
“I was about to make the change it seemed to be taking too long and it proved costly at that point for us with the stitches.
“But I’d like to see the challenge again that caused the damage to his leg which they got a throw-in from it looked as though he got a bad gash on his shin.”
On the performance McNamara said; “I’m proud of the players the way they responded. I thought a lot of things went against us today but we stuck to our task right to the end despite the disappointments and the setbacks in the game.”