A brace apiece from the irrepressible Mo Salah and Roberto Firmino, either side of a Sadio Mané strike, had the Reds cruising at Anfield.
Roma's dismal start to the second half was compounded when Di Francesco was seen exchanging angry words with midfielders Radja Nainggolan and Kevin Strootman.
Not for Liverpool fans looking for revenge because, for me, they're among the best supporters in the world just because of Roma's pure history they'll go for it again.
Two goals. Two assists. Klopp's team just continued to play long passes into wide areas, and Roma's rather slow central defenders were run ragged.
The guys respond to your tweets about Liverpool's win over Roma, with questions about Mo Salah, strategy for the second leg and more.
On fan behaviour and the suggestion there could be more trouble involving Liverpool supporters, Klopp said: "Since I've been here I've never heard anything about that".
'Tsunami' of match-fixing in lower-level tennis, says report
In fact, according to the TIU's annual report of 2017, the numbers of prima facie "betting alerts" actually went down past year . The report surveyed over 3,200 tennis players and found that 14.5% indicated they had first-hand knowledge of match-fixing.
Salah's importance was further demonstrated by the fact Roma scored the two goals that give them a slither of hope of turning the tie around, after he had been substituted.
The worldwide pop star, who is now touring to promote his album "Flicker", caught the dramatic finale of the first leg of the Champions League final between the Reds and Roma.
Di Francesco's side had lost their quarter-final first leg 4-1 at Barcelona but advanced with a 3-0 win at home where they have not conceded a goal in this season's Champions League.
The Ballon d'Or has gone to a victor of the Champions League for the last four years. I think it was hard for us in the last 15 minutes, they came out on the attack and had a lot of confidence.
"That's a massive game for us and we need to be ready for that, and we try everything to be ready for that".
"We go there with a three-goal advantage but it will be hard given what they did against Barcelona in the last round". The Italian global criticised the hosts for not showing the courage to go toe-to-toe with them in the middle of the park, instead choosing to completely bypass the midfield and try to get Mane and Salah running the channels.