Celtic needed 76 minutes to break down St Mirren and progress to the quarter finals of the CIS Insurance Cup.
Riordan made his first start for Celtic
St Mirren goalkeeper Tony Bullock made three good saves to thwart Craig Beattie in the first-half, while Ian Maxwell hit the bar for the visitors.
Beattie also hit the woodwork after the interval but the striker was not to be denied and beat Bullock with a shot.
Maciej Zurawski, who had an earlier effort ruled offside, poked in a late second goal for the cup holders.
Celtic made eight changes from the team that earned a 1-0 win over Dunfermline at the weekend.
Derek Riordan was handed his first start since his summer move from Hibs and Bobo Balde made a timely return from injury ahead of Saturday's Old Firm encounter.
And the towering Celtic defender was called upon to clear a dangerous header from Billy Mehmet early in the game.
Beattie, getting a chance to impress up front, got the first glimpse of goal for Celtic but Bullock held on to his strike.
Beattie then connected with a Paul Telfer cross but Bullock was able to push over the striker's close range header.
Celtic were given a scare on 23 minutes when Maxwell's header from a Simon Lappin corner crashed against the crossbar.
Riordan saw his half-volley whistle over the top and Bullock made another fine stop to keep out a fierce Beattie shot, with David Van Zanten on hand to clear the loose ball.
St Mirren were a menace on the break and Celtic keeper Artur Boruc was at full-stretch to clutch Lappin's drive at the second attempt.
Saints substitute Mark Corcoran did well to skip past two Celtic players after the interval but his tame effort was smothered by Boruc.
Riordan shot wide after good worrk from sub Aiden McGeady before Beattie rattled the crossbar from a tight angle.
Zurawski was denied the opener by the linesman's flag but Celtic made the breakthrough soon after.
Beattie, who had been the game's liveliest player, was eventually rewarded when he squeezed a shot beyond Bulloch from 16 yards.
Zurawski settled the match four minutes from time with a low strike from close range after a McGeady effort deflected into his path.
Celtic: Boruc, Telfer, Balde, McManus, O'Dea, Riordan, Sno, Jarosik (McGeady 45), Pearson, Zurawski, Beattie. Subs Not Used: Marshall, Nakamura, Cuthbert, Vennegoor of Hesselink.
Booked: Jarosik. Goals: Beattie 76, Zurawski 87.
St Mirren: Bullock, van Zanten, Millen, Maxwell, Broadfoot, Mehmet (Sutton 70), Murray (Iain Anderson 81), Brittain, Reid, Kean (Corcoran 61), Lappin. Subs Not Used: Smith, McGowne.
Ref: K Clark