The Tangerines were no match for their Celtic counterparts who cruised through to the quarter-finals.
From the kick-off Celtic controlled proceedings, taking only six minutes to take the lead when Joe Thomson volleyed home from 20-yards.
On 17 minutes, Paul McMullan directed a header straight at United keeper Ryan Booth.
Six minutes later Scott Findlay had the ball in the net, but was ruled offside.
A second goal was only temporarily delayed, Jamie Robson having the misfortune to turn a cross into his own net three minutes later.
Just before the hour mark, Paul McMullan slotted in a third after the United defence failed to clear a corner.
Five minutes later, only a terrific stop by Booth denied Thomson.
Nine minutes after the restart, a Liam Henderson effort struck post from 22 yards.
But Celtic weren’t to be denied a third, McMullan sweeping the ball home after a Jack Breslin cross wasn’t dealt with properly just before the hour mark.
Henderson hit the woodwork again five minutes later and Booth thwarted Thomson, Kieran Tierney and McMullan to restrict the vistors to a three goal winning margin.
Indicative of Celtic’s dominance, United’s only real chance of the game came six minutes from time when Ola Adeyemo’s downward header was only saved by keeper Jordan Hart at the second attempt.
TEAM:
Booth, Spark, Robson, B Smith, McLaughlin, H Smith, Tumilty, Duke (Malaga 71), Adeyemo (M Smith 87), Lochhead, Coote (Montgomery 56).
SUB NOT USED:
Clarkson (gk), McNaughton.