Daizen Maeda marked his 100th Celtic appearance with a match-winning hat-trick as the holders saw off a spirited challenge from Livingston to reach the Scottish Gas Scottish Cup semi-finals.
Maeda put Celtic ahead for the third time in the 86th minute to take his tally for the club to 27 goals after the cinch Premiership bottom side had twice equalised at Celtic Park through Daniel MacKay and Tete Yengi.
Substitute Kyogo Furuhashi was on target deep into stoppage time as Celtic sealed a 4-2 triumph.
Celtic missed both Callum McGregor and Cameron Carter-Vickers through injury, but they did just enough to seal a Hampden trip next month.
Carter-Vickers was withdrawn as a precaution after the defender’s hamstring caused concern in training, while Luis Palma failed to shake off a knock, which allowed Nicolas Kuhn to make his first start at Celtic Park.
Livingston also had injury issues to contend with, mainly in midfield. Jason Holt dropped out through illness and Andrew Shinnie with a groin problem, while the cup-tied David Carson joined Scott Pittman on the sidelines.
David Martindale lined up with full-back Jamie Brandon and winger Steven Bradley as part of his central trio.
Celtic had an early warning when Ayo Obileye hit the post, although Willie Collum blew for a home free-kick.
Kuhn had already shown flashes of promise before setting up the seventh-minute opener with an excellent cross from the right.
Right-back Michael Nottingham allowed Maeda to go but the forward was level when the cross came in and he took a touch before finishing from six yards.
Livi levelled five minutes later after Cristian Montano’s ball in between Stephen Welsh and Alistair Johnston put MacKay in behind.
The winger, who scored against Celtic for Inverness in last year’s final, had time to wait for the ball to bounce before curling into the top corner.
Left-back Montano undid his good work 10 minutes later when he dithered in possession on the edge of his box after Livi appeared to have thwarted a dangerous counter-attack.
Matt O’Riley won the ball back and Maeda stooped to head home after Michael McGovern had stopped the midfielder’s shot.
Celtic had chances to enjoy a more comfortable half-time break with Adam Idah the biggest cuplrit, making a mess of two shooting chances when he got in behind, although he forced a good stop with a header.
McGovern also saved well from Maeda twice before the break and both the Japan international and Idah failed to convert a low cross from Kuhn after the interval.
Yengi stabbed Stephen Kelly’s cross just wide before netting Livingston’s second equaliser in the 54th minute.
O’Riley was caught in possession by Brandon on the halfway line and, although the Celtic midfielder got back to hold up Yengi, the striker turned and curled a brilliant finish into the far corner.
The home support were almost stunned further moments later when Nottingham’s header was stopped by Joe Hart’s foot on the line.
Celtic took time to react and McGovern was equal to efforts from Johnston and Kuhn when they got going.
Furuhashi, Daniel Kelly and James Forrest – making his first appearance of 2024 – came on and the latter added a spark before being involved in taking the lead for a third time.
The winger fed Tomoki Iwata’s run beyond and the Japanese midfielder’s low cross was tapped in by Maeda.
The attacker almost got his fourth, but hit the crossbar from close range and Furuhashi was played through in the closing seconds to slot home, which was initially denied, before a VAR review overturned an offside decision.