Reo Hatate opened the scoring after just 17 minutes, making no mistake from the edge of the area to lift the spirits of an expectant Celtic Park crowd.
Further jubilation followed as Liam Scales doubled the lead five minutes before the break, heading Matt O'Riley's corner past the helpless Robby McCrorie, who had twice denied Nicolas Kuhn moments earlier.
Scales almost added to his own account, and extended Celtic's lead, in the second half, only for Oliver Bainbridge to clear off the line after McCrorie was again beaten from a corner.
Yet Bainbridge was left wanting soon after as his deflection helped Kuhn find the back of the net following a weaving run inside from the touchline just before the hour.
Substitute Anthony Ralston then added a late fourth in the third minute of stoppage-time as Brendan Rodgers' side started their search for a 13th top-flight title in 14 seasons with ease.
Data Debrief: Business as usual for Hoops
Reigning Scottish champions have now won their first match in each of the last 13 seasons, with Rangers the last such team to fail when drawing 1-1 with Hearts back in the 2011-12 campaign.
Celtic have also won their league opener in 16 of the last 17 seasons, losing the other 2-1 away to Hearts in the 2021-22 season.
This victory came as no surprise, though, as when at home for their domestic curtain-raiser, the Hoops are unbeaten in 35 such games (W31 D4) since a 4-3 defeat to Morton in 1950-51.
Sunday also continued an impressive head-to-head record, with Celtic only losing one of the 12 previous occasions that they have faced Kilmarnock on the first matchday of a league season (W9 D2).
The Japanese international struck in the 78th minute, meeting Greg Taylor's pass over the top to rifle the winner into the bottom corner.
In a tight first half, Duk was denied by Kasper Schmeichel before Alistair Johnson's header was turned narrowly past the post by Jamie McGrath.
Paulo Bernardo thought he had given Celtic the lead when he scored directly from a corner, though the goal was ruled out due to a foul on Ross Doohan.
Ester Sokler had the opportunity to equalise late on, only for Cameron Carter-Vickers to turn his effort over the bar as Celtic kept an 11th clean sheet of the season.
Meanwhile, Rangers continued their recent run of fine form with a 6-0 thrashing of Kilmarnock.
It was their second win by that scoreline this season, having also beaten Ross County on matchday three, with James Tavernier opening the scoring in the 37th minute with his first goal of the campaign.
Philippe Clement's side turned up the heat after the break, with two goals in two minutes from Danilo and Hamza Igamane putting them 3-0 up.
Vaclav Cerny then drove a reverse shot into the back of the net shortly after the hour mark before substitute Cyriel Dessers scored two first-time goals to move Rangers just four points behind Aberdeen with a game in hand.
Brendan Rodgers' side defeated German side Leipzig 3-1 on Tuesday to put themselves in a strong position in the league phase of the Champions League, but their attentions returned to domestic action this weekend.
And after Aberdeen eased past Dundee, Celtic knew they must win again to reclaim top spot on goal difference.
Goals from Callum McGregor and Nicolas Kuhn ensured they did just that, although it was a battle for the champions.
"They're totally different games, more fighting football [against Kilmarnock] and what you've got to contend with," Celtic boss Rodgers told Sky Sports.
"But I thought the players were absolutely brilliant, how they had to defend the pressure. The build-up comes quite direct from behind, so they know you have to stand up to the long balls and long throws and everything else.
"The players have shown this week they can deal with all types of games. Today was a brilliant, brilliant win for us and showed another side to us."
They will next face Hearts on 23 November, after the international break.
Brendan Rodgers' side defeated German side Leipzig 3-1 on Tuesday to put themselves in a strong position in the league phase of the Champions League, but their attentions returned to domestic action this weekend.
And after Aberdeen eased past Dundee, Celtic knew they must win again to reclaim top spot on goal difference.
Goals from Callum McGregor and Nicolas Kuhn ensured they did just that, although it was a battle for the champions.
"They're totally different games, more fighting football [against Kilmarnock] and what you've got to contend with," Celtic boss Rodgers told Sky Sports.
"But I thought the players were absolutely brilliant, how they had to defend the pressure. The build-up comes quite direct from behind, so they know you have to stand up to the long balls and long throws and everything else.
"The players have shown this week they can deal with all types of games. Today was a brilliant, brilliant win for us and showed another side to us."
They will next face Hearts on 23 November, after the international break.
Rangers went into Sunday's game six points adrift of Celtic and Aberdeen, after the two pacesetters played out an entertaining 2-2 draw on Saturday.
But they never looked likely to close that gap as they produced a flat performance at Rugby Park.
They were indebted to goalkeeper Jack Butland as he made a fine save to deny Watkins early on, while Matty Kennedy was just unable to turn an inviting Corrie Ndaba cross home.
Former Rangers shot-stopper Robby McCrorie had a busier second half, pushing a Cyriel Dessers effort away before the Nigerian hit the crossbar from the resulting corner.
Those misses were punished with just three minutes remaining, Watkins outmuscling defender John Souttar from a long ball forward before prodding past Butland.
Data Debrief: Gers fall flat once more
In contrast to the lightning starts Celtic and Aberdeen have made to 2024-25, Rangers have looked laboured in the early weeks of the season and that was the case again on Sunday.
They only mustered three shots on target throughout the 90 minutes, the same amount as their hosts, and they have now been shut out in three of their eight Premiership games this term – only St Johnstone and Ross County (four apiece) have failed to net more often.
The 49-year-old scored a clinching third goal from the spot for Inverness when their 3-1 defeat of Celtic on February 8, 2000, sent shockwaves across the nation and beyond, the victory eliciting the famous newspaper headline “Super Caley go ballistic, Celtic are atrocious.”
Derek McInnes’s side are in fine form, sitting in fourth place in the cinch Premiership but with first-hand knowledge of what can happen in cup football, Sheerin believes the Ayrshire outfit have to guard against becoming an unlikely victim when they take on Paul Hartley’s League One side on Saturday.
He said: “It is nice memories. It shows you what can happen and obviously upsets do happen.
“It was a momentous occasion for the club, they were relatively new to the league and that was part and parcel of the shock as well.
“There was belief because you always have to believe as players.
“I know Paul (Hartley) spoke about not feeling any real pressure which is understandable.
“At that time, Inverness had that mindset that there was no great pressure on us, no one expected us to do anything so that took the edge of it and we tried to enjoy it as much as we could, and obviously the way it worked out was something that nobody really expected.
“Cove will come here determined to be one of the clubs who cause an upset.
“We have done our work and hopefully that will stand us in good stead and not allow a shock tomorrow. Your attitude and application has to be spot on.
“We know what they will come with, we know shocks can happen but hopefully we will not allow that tomorrow.”
Corrie Ndaba returns after a two-game ban after being controversially sent off against Hibernian.
The defender initially saw yellow for a tackle on Jair Tavares before it was upgraded following a VAR check and it left McInnes fuming as the visitors came back to draw 2-2.
It was the 24-year-old’s first red card of his career, but he insists it will have no impact in the way he plays the game.
He said: “I was a bit surprised. I don’t think it was a red card, but the referee said from the follow-through, it was a red so there was not much I could do.
“It gets a bit technical these days. Obviously I got the ball first and the follow-through has gone into his ankle.
“I didn’t really have anywhere to put my leg, but the referee has decided to give me a red card so I have to take my medicine.
“I always tackle clean, that is the way I play so I am just going to play as normal.”
Centre-back Robbie Deas is recovering from a fractured cheekbone, while midfielders Brad Lyons and Kyle Magennis remain absent after respective cartilage and hamstring problems.
Reo Hatate, Liam Scales, Nicolas Kuhn and Anthony Ralston were all on target as the Scottish champions hammered their visitors 4-0 at Celtic Park.
Celtic have won their league opener in 16 of the last 17 seasons, losing the other 2-1 away to Hearts in 2021, though Rodgers acknowledged this is just the start for the Hoops.
"I thought we were very connected, some of our passing and the speed of our game was very good," the Celtic manager told BBC Scotland.
"Defensively we were very strong, the first goal came from that counter press. I have to be so pleased for the first game of the season.
"Being at the top of the league at the end of the season is what's important but the first steps are critical and we made a really good step today."
Matt O'Riley continues to draw attention from Premier League clubs, as well as Serie A's Atalanta, as the Celtic midfielder's future remains uncertain.
The Denmark international assisted Scales' header in the first half against Kilmarnock, reminding potential suitors of his quality with transfer speculation continuing.
Rodgers is focused on adding to his Celtic squad, though, as he aims to build a side capable of competing in the Champions League and Scotland's top division.
"Currently our focus is very much the players that are here but naturally we want to improve the squad," Rodgers added.
"It's our duty to do that for the players and we'll speak about that. I will never say anything that I've not spoken to my bosses about.
"We want to take the club forward, we know the challenges that we have on every front and for that we want to improve the squad. Hopefully, we can get in the players that can help us kick on this season.
"I'd love to have more tools to have a go at the Champions League, that's one of our big goals this season. We want to get into the play-off phases and for that, we want to improve the squad."
