Arsenal, though, failed to take advantage.
A 0-0 draw at home to lowly Everton left the third-placed Gunners still six points behind Liverpool and they'll see it as a big opportunity missed.
Liverpool's Diogo Jota (left) grabbed the equaliser for the league leaders. (AP PHOTO)
Undermined by Andy Robertson's 17th-minute red card, Liverpool actually did well to earn a point at Anfield on Saturday (Sunday AEDT) - but they could even have delivered a win after sustained late pressure following Diogo Jota's equaliser in the 86th minute.
Fulham led for the first time after Andreas Pereira's 11th-minute volley deflected into the net off Robertson, who was sent off six minutes later for bringing down Harry Wilson as the last man and denying a goal-scoring opportunity.
Cody Gakpo levelled just after half-time by heading in a cross from Mohamed Salah, who registered his 100th assist for Liverpool in all competitions.
Substitute Rodrigo Muniz's flick put Fulham back ahead in the 76th, only for Jota to run onto Darwin Nunez's pass, turn his marker and drive home a finish from the edge of the area.
Manager Gary O'Neil will do well to survive his latest damaging defeat with Wolves after Ipswich won 2-1 at Molineux.
Ipswich prevailed thanks to Jack Taylor's winner in the fourth minute of stoppage time in a match between teams in the relegation zone.
O'Neil has led Wolves to only two victories in the league this season, and three since March.
The slide began at the end of last season when Wolves won just one of their last 10 league games after being knocked out of the FA Cup in the quarter-finals by second-tier Coventry.
On Monday, after losing at West Ham 2-1, O'Neil expressed his disappointment at losing the connection with Wolves' fans and also aimed some criticism at the club's owners for sanctioning the sale of many of their top players over the last two years.
There were boos at half-time and full-time at Molineux, with Wolves staying in next-to-last place and dropping three points behind third-to-last Ipswich.
Ruud van Nistelrooy suffered his first loss with Leicester - and it was a big one.
The Foxes were thrashed 4-0 at Newcastle, with Jacob Murphy scoring twice and Alexander Isak nodding in his seventh goal of the campaign. Bruno Guimaraes netted the other one.
Van Nistelrooy, the former Manchester United and Real Madrid star striker, was brought in to replace the fired Steve Cooper and earned a win and a draw — both at home — in his first two games in charge, but this felt like a rude awakening.
