Steven Gerrard kept his cool to turn up the heat on their title rivals as the midfielder's late penalty clinched a dramatic 3-2 win against Fulham.
Brendan Rodgers' men were twice forced to come from behind on a bizarre evening at Craven Cottage.
"We knew this was important," Rodgers told Sky Sports. "I said to the players these are the games where you arrive in the Champions League - games like this here. You're playing a team who are fighting, trying to stay in the division.
"We've come off the back of a brilliant performance at the weekend and tonight we've again got another three points in a different way.
"So it really shows that this team has improved in every facet of the game.
"We're just going to keep pushing and I think we've shown enough times that we're a very good side. We're chasing, but we need some of them (the teams above) to drop points before anything else can happen.
"We know we have Chelsea and Manchester City to play at home which we'll look forward to because we've been outstanding at home but we've just got to take it game by game.
"I'm enjoying watching the team improve and develop as a coach."
The victory moves them within a point of third-placed City, whose clash with Sunderland was postponed due to the bad weather, and in touch with Chelsea.
Jose Mourinho recently described his side as a "little horse" that were not ready to win the title - an argument dismissed by City boss Manuel Pellegrini and laughed off by Rodgers.
The Liverpool boss joked his side "may be the chihuahuas that run in between the horses' legs" but was quick to praise his side's attacking intent.
"Thankfully we're a very aggressive and offensive team going forward, so we have goals in the team.
"That's something I've been trying to build since I've been here. When I arrived into the club, the complaint about the team was that they didn't score enough.
"Now we know we can go to any ground, or at home, and get goals. Obviously tonight the goals got us the three points rather than our defending."
Rodgers was also swift to praise captain Gerrard and said: "Steven is peerless in many aspects of football. He was brilliant against Arsenal, dictating the game, playmaking from behind and his pass for the first goal here.
"He has that penetration he has shown all his life and then his composure at the end was not by accident. He studies the goalkeeper, which way he dives, so that professionalism is still there.
"There's no greater person than Steven Gerrard to take a penalty right at the end to get the three points and he tucked it away really well."