Chelsea tightened their grip on fourth place with a win over Tottenham, while Bournemouth had a goal ruled out by the video assistant referee at Burnley, who were awarded a penalty instead in dramatic scenes at Turf Moor.
Strikes by the returning Olivier Giroud and Marcos Alonso handed Chelsea all three points at Stamford Bridge, with an Antonio Rudiger own goal a late consolation for Tottenham.
VAR was called into action to review a dangerous tackle by Tottenham's Giovani lo Celso on full-back Cesar Azpilicueta - but no red card resulted.
The controversial system was also a big feature in Burnley's 3-0 win over Bournemouth at Turf Moor.
Cherries striker Joshua King had an early goal disallowed because of a handball by Philip Billing. Matej Vydra then opened the scoring for the Clarets with his second goal in two games, before Harry Wilson thought he had got an equaliser for the Cherries four minutes later.
But VAR ruled Bournemouth right-back Adam Smith had handled the ball inside his area in the build-up to Wilson goal. Sean Dyche's men were therefore awarded a penalty at the other end of the pitch, which Jay Rodriguez converted to double Burnley's lead. Dwight McNeil added a third late on.
- Relive all of Saturday's Premier League action
- Report: Chelsea 2-1 Tottenham
- Report: Burnley 3-0 Bournemouth
- Report: Sheffield United 1-1 Brighton
- Report: Southampton 2-0 Aston Villa
- Report: Crystal Palace 1-0 Newcastle
- Report: Leicester City 0-1 Manchester City
Manchester City missed a penalty but still overcame Leicester City 1-0 to open up a seven-point gap between second and third in the table.
Sergio Aguero had his spot-kick beaten away by Kasper Schmeichel, after the video assistant referee ruled Dennis Praet had blocked Ilkay Gundogan's strike with his arm.
Yet second-placed City, who trail leaders Liverpool by 19 points having played one game more, secured the points through substitute Gabriel Jesus.
Sheffield United missed the chance to move above Tottenham in the table and into fifth place, managing only a 1-1 draw with Brighton at Bramall Lane.
Enda Stevens' powerful drive put Chris Wilder's team on the front foot but Neal Maupay's first goal since December levelled the game within three minutes for the Seagulls.
Southampton moved a step closer to Premier League survival with a comfortable 2-0 victory over strugglers Aston Villa.
Shane Long bundled a Moussa Djenepo cross over the line on eight minutes, with Stuart Armstrong sealing victory in the closing moments after Villa goalkeeper Pepe Reina was caught upfield.
Dean Smith's Aston Villa remain a point above the relegation zone after a third straight defeat.
Patrick van Aanholt's free-kick was enough to secure Crystal Palace a 1-0 win over Newcastle at Selhurst Park.
Roy Hodgson's side move up to 13th in the table, two points clear of the Magpies, who also saw midfielder Valentino Lazaro sent off in stoppage time.