Celtic ended an unusually difficult week with a 3-1 Betfred Cup last-16 win over Partick Thistle at the Energy Check stadium at Firhill.
Striker Leigh Griffiths' goal after 17 minutes gave the dominant visitors the interval lead but that was dramatically cancelled out in the 72nd minute by Jags attacker Andrea Mbuyi-Mutombo.
However, quickfire goals from substitute Moussa Dembele and Tom Rogic got the treble-winners back to winning ways.
Brendan Rodgers' side lost 1-0 at Hearts last Sunday before being dumped out of the Champions League qualifiers on Tuesday night with a 3-2 aggregate defeat by AEK Athens.
Moreover, defender Dedryck Boyata was sent to train with the under-20s with his future in doubt after claiming an injury caused him to miss the trip to Athens, with Rodgers insisting the Belgium international was fit.
Celtic's win against their Glasgow neighbours, however, was just the result needed before they face FK Suduva in the first leg of their Europa League play-off on Thursday night.
With one eye on the trip to Lithuania, Rodgers dipped into his squad with Scott Bain, Kristoffer Ajer, Cristian Gamboa, Scott Sinclair, Mikey Johnston and Emilio Izaguirre in the starting line-up, the Honduras international playing his first game since returning to the club for a second spell.
Thistle, who dropped out of the Ladbrokes Premiership last season, almost found themselves a goal down inside five minutes when Griffiths picked out Rogic but goalkeeper Cammy Bell was equal to the Australia midfielder's drive from 12 yards.
The home side withstood some exerted pressure from Celtic thereafter but only until Sinclair went past defender Christie Elliott and cut the ball back for Griffiths to fire in from 10 yards for his first of the season and his 99th for Celtic.
The elegant Rogic drove the Parkhead men forward and in the 25th minute his clever chip at the edge of the box found Johnston but his close-range shot was smothered by Bell, who moments later gathered another effort from the Hoops youngster.
The tempo dropped towards the interval but Celtic still threatened with Bell saving a header from Rogic before midfielder Olivier Ntcham clipped the top of the bar with a 25-yard drive.
Celtic continued with their near-misses after the break with Johnston and Sinclair having efforts which came close but not close enough.
Griffiths was replaced by Dembele in the 64th minute and within moments he drew a great save from Bell with a powerful angled-drive.
Celtic were stunned when Thistle levelled.
A pass from substitute Aidan Fitzpatrick set up Mbuyi-Mutombo and, with the Celtic defence in disarray, he fired a low drive past Bain and in off the far post.
However, Dembele eased increasing nerves four minutes later when he knocked in a Gamboa cross from eight yards with his thigh, with the Hoops full-back providing a similar cross for Rogic to sweep the ball past Bell to clinch a quarter-final place.