Strikes either side of the half-time whistle from Alexis Mac Allister and Mohamed Salah - who broke yet another record on Wednesday evening - proved telling, but the scoreline certainly did not tell the full story, as the visitors asked many questions of the Liverpool backline and could count themselves unfortunate not to at least bag a consolation.
After experiencing the Champions League rendition of You'll Never Walk Alone for the first time as Liverpool manager, Slot witnessed his charges strike early against Bologna, but the Reds did not have it all their own way early doors.
Mac Allister's back-post tap-in was the difference heading into the interval, but Bologna marksman Thijs Dallinga had a strike of his own disallowed just a couple of minutes before, while Dan Ndoye crashed the woodwork twice, one via a significant deflection.
Vincenzo Italiano's backline still looked vulnerable every time Liverpool surged forward, but the beleaguered Alisson Becker was not enjoying an easy ride against the plucky Italians, who showed identical endeavour at the start of the second half.
However, there was not a shred of ruthlessness about the Bologna attack, in stark contrast to the six-time winners, who could breathe a little easier when Salah curled in a delightful second 15 minutes from the end.
In doing so, Salah became the first-ever Reds player to score in five straight Champions League home matches, but Slot will be under no illusions that his side had to count their lucky stars at times, as Bologna did themselves proud on English soil.
Liverpool are now coincidentally only behind four teams beginning with B - Borussia Dortmund, Bayer Leverkusen, Brest and Benfica - in fifth place in the League Phase table, while Italiano's side sit 26th as they bid to make it third time lucky next time around.
LIVERPOOL VS. BOLOGNA HIGHLIGHTS
Thijs Dallinga disallowed goal vs. Liverpool (9th min, Liverpool 0-0 Bologna)
It takes just nine minutes for the Anfield net to ripple for the first time in this season's Champions League, but Thijs Dallinga just had to time his run a little better!
The former Toulouse man - who netted in both of his side's clashes with the Reds last season - beats Alisson Becker from a tight angle with a low effort through his legs, but Liverpool's line is good, and the Reds catch the Dutchman offside.
Alexis Mac Allister goal vs. Bologna (11th min, Liverpool 1-0 Bologna)
The true definition of a sucker punch! Just two minutes after Bologna think that they have broken the deadlock on Merseyside, Slot's crop are off the mark.
An incisive passing move through the middle ends with Darwin Nunez spraying the ball out to Salah, whose delightful chipped cross finds the unchecked run of Mac Allister, who has the simplest job of tapping in at the back stick.
Lukasz Skorupski was given no protection whatsoever from a static Bologna defence, and there was little that the Rossoblu goalkeeper could have done with both Mac Allister and Luis Diaz queuing up.
Darwin Nunez disallowed goal vs. Bologna (17th min, Liverpool 1-0 Bologna)
Both number nines have a strike ruled out in the opening 20 minutes, as Nunez is put clean through by a sublime ball from Trent Alexander-Arnold and finishes well, but the linesman's flag cuts Liverpool's celebrations short.
Mohamed Salah goal vs. Bologna (75th min, Liverpool 2-0 Bologna)
Liverpool have narrowly escaped a couple of scares in the second half, but Bologna's attack has lacked the individual brilliance of Salah, who makes Liverpool history in front of the Kop.
The Egyptian takes the ball on the right-hand side of the area, and as Alexander-Arnold makes an overlapping run, space opens up for Salah to cut inside as Bologna's defenders are distracted by the right-back's movement.
Salah opens up his body, aims for the top corner and finds it with panache, thereby becoming the first Liverpool player to score in five successive Champions League home matches.
MAN OF THE MATCH - RYAN GRAVENBERCH
A word for Mac Allister and Salah of course - as well as the energetic Dominik Szoboszlai - but the rejuvenated Ryan Gravenberch ran the show in midfield once again for Liverpool and was here, there and everywhere against the Rossoblu.
Showcasing his newfound confidence to its maximum, the Dutchman completed three successful dribbles - always looking to drive his team forward - while also creating two chances and completing 89% of his passes. Like a new signing?
LIVERPOOL VS. BOLOGNA MATCH STATS
Possession: Liverpool 52%-48% Bologna
Shots: Liverpool 9-12 Bologna
Shots on target: Liverpool 4-2 Bologna
Corners: Liverpool 5-3 Bologna
Fouls: Liverpool 10-8 Bologna
BEST STATS
WHAT NEXT?
The 12.30pm kickoff awaits Liverpool once again this weekend, as the Reds head to Crystal Palace for Saturday's early Premier League offering, and their next European game comes away to RB Leipzig on October 23.
Meanwhile, Bologna host Parma in Serie A action on Sunday, before their second straight trip to English opposition in the Champions League on October 22, when they take on Aston Villa.