As early as the fourth minute Daniel Lyons directed a header just wide of goal while Paul McDonald then wasted his opportunity from a close-range header.
DC's stand-in skipper David Munster also tested goalkeeper Scott Fox with a headed attempt in the 20th minute.
Kevin Gawley had Celtic's best first-half chance in the 26th minute after a Ryan Conroy cross but his weak shot didn't trouble Declan Brown.
The home side had a penalty claim turned down before the break when Paul McVeigh appeared to be bundled over in the box.
Riordan was always Celtic's main attacking threat and he very nearly caught out goalkeeper Brown with an audacious long-range lob before the break.
Substitute goalkeeper Harbinson denied Riordan in the 68th minute and young defender Ciaran Caldwell then clearned off the line after the Celtic striker had rounded the DC custodian.
Riordan could not be denied in the 83rd minute after he superbly turned to strike Michael McGlinchey's cleverly flicked pass into the bottom corner.
Right at the end new DC signing Liam Watson, better known for his hurling exploits with Antrim, drove a long-range effort inches over the crossbar.
Donegal Celtic
: Brown, Heagney, Gargan, McClean, Caldwell, Bradley, Munster, Lyons, Armstrong, McDonald, McVeigh.
Subs
: Harbinson for Brown 65; Bonner for Heagney 59; Hanna for McClean 65; Duff for Caldwell 78; Kearney for Lyons 59; Fegan for McVeigh 76; Lavery for Armstrong H-T; Thompson for Caldwell 83; McCabe for Gargan H-T
Celtic XI
: Fox, Towell, Conroy, Ferry, Cuthbert, Lafferty, McGlinchey, Millar, Riordan, Gravesen, Gawley, Gaughan.
Subs
: Gaughan for Towell 69; Graham for Gawley 77; Monti for Gravesen 85
Referee
: Ray Crangle (Belfast)