Liverpool beat Premier League basement club Sheffield United 2-0 on Wednesday to move just two points behind leaders Arsenal as Fulham hammered Nottingham Forest 5-0, heaping the pressure on manager Steve Cooper.
Elsewhere on a busy programme in the English top flight, Brighton beat Brentford 2-1 and Bournemouth overcame Crystal Palace 2-0.
Struggling Manchester United hosted Chelsea in the later kick-off as champions Manchester City made the trip to Aston Villa, who boasted 13 home league wins in a row.
Virgil van Dijk scored opened the scoring at Bramall Lane, turning home a Trent Alexander-Arnold corner in the 37th minute from near the penalty spot.
Liverpool dominated possession but were made to sweat by Sheffield United until midfielder Dominik Szoboszlai made the points safe in time added on.
The victory takes Jurgen Klopp's team to 34 points -- just two behind Arsenal, who beat Luton 4-3 on Tuesday.
It was a miserable first game back in charge for manager Chris Wilder, who returned to the club on Tuesday following Paul Heckingbottom's dismissal -- the first sacking of the season.
Sheffield United have been defeated 12 times in 15 games and are four points from safety.
Nottingham Forest, in their second season back in the Premier League, have now lost four matches in a row.
Alex Iwobi and Raul Jimenez scored two goals apiece and Tom Cairney completed the humiliation in the final minutes.
Brighton recorded a 2-1 home win against Brentford courtesy of goals from Pascal Gross and Jack Hinshelwood.
Bournemouth notched their third win in four league games, with Marcos Senesi and Kieffer Moore on the scoresheet at Palace.
Marcus Rashford paid for his slump in form as the Manchester United star was dropped to the bench by Erik ten Hag for the match against Chelsea at Old Trafford.
Rashford was one of the shining lights of Ten Hag's first campaign in charge, scoring a career-high 30 times last season.
However, the England forward has struggled to rekindle that form this term, scoring just two goals so far.
Wolves beat Burnley 1-0 on Tuesday.
On Thursday Everton host Newcastle while West Ham travel to Tottenham.
