Second half goals from Jack Aitchison and Broque Watson settled the points for Michael O’Halloran’s side who have played four matches without losing a goal.
Aitchison opened the scoring with a low shot from the edge of the penalty box following good build up play down the right involving Watson and substitute Kenny Mearns.
Watson put the result beyond doubt with a close in effort after another substitute, Grant Thorburn had charged down the left wing.
“It was a good performance across the team, at this level it’s about performances as much as results,” O’Halloran said.
“Last week I was a bit critical of the team straight after the match but on reflection it’s maybe best to give it 24 hours to review things.
“Against Hearts (the previous week) we created a lot of first half chances but lacked a bit of composure around goal. Michael Johnston hit the woodwork after a move involving 18 passes.
“There’s a bit of composure missing around goal but we’re building a platform for individuals to develop. We want to play the Celtic way and see players pushing on ready for the next level.
“Dundee United are a good side but we were worthy winners, we’ll take a lot from the match, work hard in training and look to improve in the next match against the Fife Elite Academy.
Sunday’s match will be at Lennoxtown with a 2pm kick-off, tonight at Cappielow Celtic face Dundee in the Development League, kick-off 7pm.
CELTIC: Conor Hazard; Steven Welsh, Wallace Duffy, Blair Kidd (Dylan McKendry), Dan Church; Ross McAllister, Lewis Bell; Jack Aitchison, Michael Johnston (Kenny Mearns), Broque Watson; Kieran McGrath (Grant Thorburn)