Joe Ledley and Anthony Stokes netted against St Mirren to put Celtic into Monday's Scottish Cup semi-final draw.
Ledley's close-range header from James Forrest's cross gave the visitors a fifth-minute lead.
Emilio Izaguirre's blunder allowed Saints' Esmael Goncalves to level soon after, before Stokes headed home another Forrest delivery.
St Mirren pressed without success in the second half and Celtic's Gary Hooper fired against the crossbar.
It was just 34 days since St Mirren defeated Celtic 3-2 in the Scottish Communities League Cup semi-final at Hampden.
Celtic's Stokes had the game's first real chance on three minutes, profiting from Hooper's headed flick-on to run through the centre before being closed down quickly by St Mirren's defence.
However the visitors ensured their next attacking move had an end result.
Forrest tricked his way past Saints' Paul Dummett on the right and provided the cross for Ledley to head home on the six-yard box.
But any hopes Celtic had of this cup tie being a straightforward affair were extinguished when St Mirren hit back on 13 minutes.
Izaguirre looked to have Lee Mair's long diagonal ball covered but, under pressure from Steven Thompson, the Honduran's unsure first header was followed by a catastrophic one as he knocked it over onrushing keeper Fraser Forster, leaving Goncalves to nod into an empty net.
St Mirren Park was buzzing but Celtic tempered that in the 21st minute with a goal straight from the training ground.
Forrest's short corner to Hooper was returned to him and the winger dinked it to the far post where Stokes arrived unmarked to head in off the post.
The game was then given an opportunity to get its breath back before Efe Ambrose's slaloming run into the box ended with a blocked shot on 40 minutes.
Matthews and Hooper combined to set up captain for the day Ledley at the beginning of the second half, but the Welshman's tame effort was gathered easily by Samson.
St Mirren began to impose themselves on their visitors on the hour mark, when a series of corners led to Victor Wanyama blocking well from another Goncalves strike.
Mair misread an Ambrose header in the 68th minute which allowed Hooper to run clear and put his laces through a shot which Samson turned onto the bar.
Then it was Forster who had to be alert, rushing out to thwart Thompson.
Saints' midweek goal hero Graham Carey replaced Paul McGowan and, with 10 minutes remaining, he forced Forster into an excellent diving save from a whipped free-kick.
Kelvin Wilson cleared well from Gary Teale's cross in the closing stages, with the ensuing St Mirren corner presenting Mair with a great chance at the back post, but the defender could only slam in into the side-netting.
And it proved to be the home side's last opportunity as Celtic progressed to the semi-final stage.