Chelsea beat Leeds United 3-1 in front of 2,000 spectators at Stamford Bridge while Manchester United fought back from a goal down to win 3-1 at West Ham United -- their fifth straight comeback victory on the road -- in front of the same size crowd.
Clubs in less restricted areas of England were allowed to welcome back 2,000 fans but in higher risk places games carried on behind closed doors with Manchester City beating Fulham 2-0 and Everton held to a 1-1 draw at Burnley.
Chelsea moved top of the table as they came from behind to beat Leeds United 3-1 at home, set on their way by a fifth goal in four days from French forward Olivier Giroud.
Giroud, 34, marked his first league start of the season - reward for his four goals in Chelsea's thrashing of Sevilla in the Champions League - by stretching to turn in a whipped cross by Reece James in the 27th minute.
That cancelled out a fourth-minute opener for Leeds by Patrick Bamford.
Chelsea went ahead in the 61st minute when Kurt Zouma jumped higher than everyone to power a Mason Mount corner into net and Christian Pulisic sealed the win in added time when he turned in a cross by Timo Werner.
The win pushed Chelsea up to top spot with 22 points, leap-frogging Tottenham Hotspur and Liverpool who both have 21 and play on Sunday.
Manchester United moved up to fourth after recovering from a poor first-half display at West Ham.
Czech midfielder Tomas Soucek put the hosts ahead in the 38th minute, turning in at the back post after Declan Rice had headed on a corner.
United were well below their best, forcing Ole Gunnar Solskjaer to bring on Marcus Rashford and Bruno Fernandes from the bench at the break and although the Norwegian had been hoping to rest his key players ahead of Tuesday's Champions League crunch match in Leipzig, the move paid off.
Portuguese midfielder Fernandes set up Paul Pogba for the equaliser in the 65th minute, the French midfielder scoring with brilliant side-foot curler from outside of the box.
Mason Greenwood put United ahead with a superb short on the turn and Rashford completed the comeback in the 78th minute with a delicate chip.
Manchester City are fifth after first-half goals from Raheem Sterling and Kevin de Bruyne secured a comfortable home win over struggling Fulham.
Only a string of superb saves from Fulham goalkeeper Alphonse Areola denied City a bigger win after Sterling fired the hosts ahead and De Bruyne converted a 26th-minute penalty.
Dominic Calvert-Lewin cancelled out Robbie Brady's opener as Carlo Ancelotti's Everton earned a point at Turf Moor.
Burnley grabbed the lead in the third minute when Ashley Westwood fed Brady who drilled the ball into the bottom corner from the edge of the box.
Calvert-Lewin brought Everton level on the stroke of halftime, sliding in to meet a low cross by Richarlison for his 11th league goal of the season.