Liverpool made it two wins from two in the new Champions League format as goals in either half from Alexis Mac Allister and Mohamed Salah secured a routine 2-0 win over Bologna at Anfield.
Mac Allister converted Salah's cross from close range after 11 minutes to put the hosts ahead, but the visitors had their chances before the interval as Alisson denied Kacper Urbanski while Dan Ndoye struck the base of the post.
But Salah settled any nerves in the second period as he notched for the fifth successive Champions League home game, collecting Dominik Szoboszlai's pass before cutting inside Juan Miranda to thunder his strike into the top corner (76).
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It is a measure of how well Arne Slot has settled in that this result means he has become the first Liverpool boss in history to win eight of his first nine matches in charge.
Slot told TNT Sports: "It's hardly impossible to do something special at this club. It wasn't an easy win, in my opinion. Bologna made it difficult. They man-mark all over the pitch, so you have to wait for the right moment, because if you play through it, then it's completely open."
Saturday's victory at Wolves demonstrated they can win when not at their very best, an important quality amid such a hectic fixture schedule, and this latest triumph was again achieved with minimum fuss ahead of this weekend's trip to face Crystal Palace in the Premier League.
The result moves them up to fifth place in the nascent league table with Bologna down in 26th position. The Reds face a trip to RB Leipzig on October 23 in their next European outing.
Bologna will be back in England again in just under three weeks as their next game in this competition is at Villa Park a day earlier.
How Slot continued his fine start
An early kick-off at Palace on Saturday will provide another tough test, but Liverpool will go into the game top of the table and with another away victory on their minds.
Against Bologna, they had to survive some nervous moments in a hard-fought clash. Thijs Dallinga and Darwin Nunez both had efforts ruled out for offside, and the Italians - in their first ever Champions League campaign - acquitted themselves very well.
Ndoye struck the post moments before Bologna capitalised on an error in his own penalty area from Trent Alexander-Arnold, but Alisson - on his 32nd birthday - saved to deny Urbanski.
Riccardo Orsolini was also denied by the Brazilian on his 50th European appearance for Liverpool before Salah inevitably had his say.
The Egyptian's sumptuous strike was his 49th Champions League goal, as he cut in onto his left and curled his shot into the top corner to ensure Slot continued his fine start to his tenure.
The Dutchman added: "They worked really hard to keep a clean sheet again today, though we also needed our goalkeeper on a few occasions.
"We scored two very good goals, especially the second one. It is always difficult to play a team takes that much risk and is constantly on top of you. Overall, a good result, but I wouldn't use the word delighted myself today."
Analysis: Salah settles Liverpool nerves
Sky Sports' Ben Grounds:
Liverpool are one of only seven teams in the 36-team competition with a 100 per cent record but Bologna were not overawed by their first trip to Merseyside and from the off committed five men to a high press.
Even after Liverpool took an early lead they found it difficult to play their way out from the back and had it not been for Alisson and the frame of the goal they would have been in more trouble.
It seemed Liverpool would overwhelm their opponents after Mac Allister's opener but Slot's side then lost their way as Ndoye, Bologna's main threat, twice hit the woodwork.
It was Salah's timely late intervention that made sure of a victorious return of the Champions League to Anfield.
The night was far from straightforward for the hosts but for the ninth time in as many appearances in this competition, Salah scored to ease the anxiety with 15 minutes left.
The 32-year-old is out of contract at the end of the season but here was another reminder of his importance, how well he took his sixth goal in four appearances against the Serie A side.
Mac Allister: There is room for improvement
Liverpool midfielder Alexis Mac Allister told TNT Sports:
"It is clear we are in transition, we are happy with the ideas, we are trying to get there. There is room for improvement, that's why we work very hard every day.
"I'm really happy personally but for the team. He [Alisson] made some good saves. Sometimes I think we need to defend better, at least Ali showed how good he is. I'm happy for him and for the team."
Liverpool goalkeeper Alisson Becker told TNT Sports:
"We were up against a fantastic opponent, it was really tough. They play really well with the ball and without the ball they are competitive. We did well to manage their game, scored enough to win the game and defended well to keep the clean sheet."
On Salah, Alisson added: "He's a player that helps us a lot, sometimes it looks like he's not in the game but suddenly a perfect touch, he puts the ball in the top corner. That's his quality, his strength as well.
"We are lucky to have him but we always have to highlight the hard work the team had and a lot to improve but good enough to win the game."