Match ends, East Kilbride 0, Celtic 2.
Celtic ended East Kilbride's memorable Scottish Cup journey but the Lowland League side exit with heads held high.
Two scrappy goals from corners were their undoing, the first bundled in via the hand of Leigh Griffiths.
Deadline-day signing Colin Kazim-Richards scrambled in his first for the club early in the second half.
East Kilbride's defending was often heroic and goalkeeper Matt McGinley did his chances of progressing up the football career ladder no harm either.
This may not be the last we see of the plucky South Lanarkshire side - four tiers below Celtic in the Scottish football pyramid - on the big stage.
Captain Barry Russell - East Kilbride born and bred - generally held the back line together and his charges occasionally knocked the ball about nicely without creating anything clear cut.
The textbook rule when a footballing minnow takes on a giant is not to concede early and East Kilbride's resolve had to be applauded during the first half.
Their defence repelled everything that came at them for 20 minutes.
Charlie Mulgrew, back for the Premiership side after injury, headed over before two East Kilbride players took one for the team in ensuring their goalmouth was not breached in the opening exchanges.
Martin McBride felt the ball full force in his stomach to concede a corner before Scott Stevenson followed in making a last-ditch clearance.
Doubts were cast over Griffiths' ability to continue when he was fouled by Craig Howie - indeed EK boss Billy Ogilvie lightheartedly told the striker to just go off as they crossed paths at the side of the pitch.
But just as Celtic manager Ronny Deila readied substitutes, Griffiths popped up to put Celtic ahead with his 28th goal of the season.
However the ball appeared to go in via the Scotland forward's arm from a yard out following Dedryck Boyata's header from a corner.
Despite that apparent injustice the Kilby team did not crumble.
Goalkeeper McGinley - a PE teacher by trade - dived to deny James Forrest, then punched away the ensuing corner.
Kazim-Richards eased any lingering nerves from the Celtic supporters - who appeared to boo their side at both half-time and full-time - 10 minutes after the interval.
Another corner and a Griffiths overhead kick prompted another scramble, and Stevenson's attempted clearance only fell to the Turkish international, who forced it home.
But the floodgates did not open for Celtic, mainly thanks to the manful efforts of Russell and McGinley.
Jack Smith had one shot on target for East Kilbride before Scott Brown hit the outside of the post near the end for Celtic.
- 4HowieBooked at 15mins
- 7HastingsSubstituted forGormleyat 63'minutes
- 10BradyBooked at 31minsSubstituted forMillarat 90'minutes
- 11JohnstoneSubstituted forTempletonat 85'minutes
- 16Mackay-StevenSubstituted forAllanat 69'minutes
- 21MulgrewSubstituted forBittonat 77'minutes
- 9GriffithsSubstituted forChristieat 81'minutes
- George Salmond
- Shots on Target
Second Half ends, East Kilbride 0, Celtic 2.
Kieran Tierney (Celtic) wins a free kick on the right wing.
Foul by Jack Smith (East Kilbride).
Substitution, East Kilbride. Gavin Millar replaces Anthony Brady.
Hand ball by Scott Allan (Celtic).
Substitution, East Kilbride. Marc Templeton replaces Frazer Johnstone.
Foul by Scott Brown (Celtic).
Anthony Brady (East Kilbride) wins a free kick in the attacking half.
Scott Brown (Celtic) hits the right post with a right footed shot from outside the box.
Substitution, Celtic. Ryan Christie replaces Leigh Griffiths.
Martin McBride (East Kilbride) wins a free kick in the attacking half.
Foul by Colin Kazim-Richards (Celtic).
Scott Allan (Celtic) wins a free kick in the defensive half.
Foul by Frazer Johnstone (East Kilbride).
Substitution, Celtic. Nir Bitton replaces Charlie Mulgrew.
Foul by Efe Ambrose (Celtic).
Liam Gormley (East Kilbride) wins a free kick in the defensive half.
Attempt missed. James Forrest (Celtic) right footed shot from the centre of the box is close, but misses to the left.
Corner, Celtic. Conceded by Gavin Lachlan.