Liam Scales provided an assist as Celtic survived a scare from fellow Irishman Conor Sammon to make it Into the last 16 of the Scottish Cup but landed Ange Postecoglou with another trio of injury worries.
Goals from Giorgios Giakoumakis, assisted by Scales, and Liel Abada before the break appeared to put the visitors on easy street against a well-organised Alloa outfit but Barry Ferguson’s men struck with 15 minutes left to make it more nervy than it should have been.
And when the dust settled, the Hoops boss was left sweating over the loss of Callum McGregor, Yosuke Ideguchi and Abada, all of whom went off injured.
Postecoglou made six changes from the side that beat Hibs on Monday but he still fielded a strong line-up against an Alloa outfit currently lying eighth in League One.
Giakoumakis led the line either side of Abada and Daizen Maeda but Reo Hatate, who had such a fine debut against Hibs, was on the bench, alongside Christopher Jullien, making his first squad appearance in 13 months after suffering cruciate ligament damage.
As expected, Celtic dominated possession but they hadn’t troubled Alloa until they struck ruthlessly in the 13th through Giakoumakis.
The Greek striker darted to the near post to cleverly divert Liam Scales’ excellent left wing cross past David Hutton.
Liel Abada found the net shortly afterwards, but the Scottish heavyweights were left sweating following a Sammon header in a nervy ending.
Get the latest sports headlines straight to your inbox by signing up for free email alerts