The result means that the Rossoneri have dropped yet more points and could fall as far as eight behind Inter andseven behind Juventus heading into the break.
Injuries to Anthony Martial and Jesse Lingard dented United's attacking thrust and PSG scored twice in seven second-half minutes at Old Trafford on Tuesday to put a foot in the quarter-finals.
Arsenal paid the price for missing a host of opportunities and were punished as Liverpool grew increasingly dangerous, the deadlock broken when Trent Alexander-Arnold's free-kick glanced in off Kiwior's head with seven minutes left.
But while Arsenal got off to a good start, they failed to kill the game and that allowed Matheus Cunha to pull one back in the 86th minute to set up a tense finish at a freezing Emirates Stadium.
Messi's one weakness was also exposed as he failed to find the net from the penalty spot seven minutes before half-time. However, he settled the visitors' nerves by drilling home with the aid of a deflection just after the break.
The 34-year-old, who re-joined Inter on a 12-month deal this summer, opened the scoring in the 19th minute with a cool side-footed finish. Oscar Gloukh levelled for the visitors in the second half.
In a relentless and frantic game, fuelled by wicked rain and wind on Merseyside, Liverpool took swing after swing at Newcastle in the first half but were in danger of being held to a third consecutive Anfield draw.
And the Senegal international then doubled the advantage in the 35th minute after a superb turn, before Firmino tapped home to round off a brilliant counter-attack on the stroke of half-time.
William Troost-Ekong had put Nigeria ahead seven minutes before the end of a cagey first half when the centre-back rose highest to powerfully head in from nine yards out following a corner.
Yet Juventus produced a dramatic recovery in the final half-hour, starting with Dybala halving the deficit with a cool finish following a defensive mistake by the German side.
Goals from Rakitic and Messi put Barca 2-0 up inside seven minutes but Mateo Kovacic reduced the deficit shortly after and Marco Asensio equalised nine minutes before half-time.
After notching a first-half hat-trick, the Portuguese star turned home Gareth Bale's cross in the 61st minute to score his fourth and take his tally to 229 goals, moving him past previous record holder Raul on the club's scoring charts before