The Reds came back twice at Craven Cottage before captain Steven Gerrard scored a dramatic stoppage-time penalty winner to take them to just four points off Premier League leaders Chelsea.
Sky Sports expert Niall Quinn told Match Choice that the win puts Brendan Rodgers' side in the mix for the title.
He said: "It's a big, big win especially with Chelsea messing up, Arsenal as well didn't get the victory and this win propels them in to the title race for me.
"They also had a great result at weekend thrashing Arsenal. The manager will probably play it all down of course but to go away on a cold, wet and very windy night, to be down twice and to have I suppose the drive and resolve to go and get the victory will count for a lot and I for one enjoyed a great game of football but it was heart breaking for Fulham.
"For it to be a great year for Liverpool they may look back on this game and say what a pivotal moment it was because they came back twice and to go on and snatch it at the end - they're the type of games and wins that really add up to something special at the end and Liverpool fans are dreaming."
The race for this season's league title is still wide open and with the top three of Chelsea, Manchester City and Arsenal all dropping points within the week, Quinn believes Liverpool are contenders in the most exciting title tilt we've seen in over two decades.
"Liverpool are bang in it, they've been excellent and they're a credit to what I believe is the greatest league since certainly I was playing in the original Premier League; it's just been terrific all year.
"Arsenal had a tough game against a stubborn Man United, they got a point but that's two points gained again by Liverpool, so they've gained five points on Arsenal in the league in a few days; Liverpool are right back in it. Spurs had a great result to keep their results alive.
"The pressure on the top that each club is coming out with is fantastic."