Chelsea's win, which came after two draws, lifts them to 22 points -- one behind City and three clear of fourth-placed Arsenal ahead of the later kick-offs on Saturday.
They have won 15 out of 17 games in all competitions since the Dutchman replaced Juergen Klopp in the close season.
Newcastle United manager Eddie Howe praised his team's hard work and mentality as they beat Arsenal 1-0 at home after taking an early lead on Saturday.
The defeat dropped City to second spot, two points behind Liverpool who recovered to beat Brighton & Hove Albion 2-1.
Mikel Arteta's Gunners remained provisionally third in the standings on 18 points, with the two teams above them -- Manchester City and Liverpool -- playing later on Saturday. Newcastle climbed to eighth on 15 points.
Five of the 10 top-flight games in England last weekend saw the result change in stoppage time, including Brentford's 4-3 win over Ipswich and West Ham's 2-1 defeat of Manchester United -- Erik ten Hag's last match as boss of the Red Devils.
England winger Madueke hauled Chelsea level but the hosts couldn't find a winner despite their numerical advantage in the closing stages.
Liverpool will head into the international break top of the Premier League after a 1-0 win at Crystal Palace before champions Manchester City and Arsenal both recovered from going behind to claim home wins on Saturday.
Liverpool took the lead after nine minutes when Cody Gakpo ran on to Tsimikas' through ball down the left and centred for Jota, who breezed past Palace debutant Trevor Chalobah to poke home from close range.
Chelsea, who won 1-0 at Bournemouth last Saturday, moved into second place in the Premier League table ahead of the rest of the weekend's fixtures. West Ham, under new coach Julen Lopetegui, are 14th.
Arsenal players are unfazed by Manchester City striker Erling Haaland's goal-scoring rampage, midfielder Jorginho said vouching for the Gunners' confidence ahead of Sunday's Premier League clash with City.
The Gunners shrugged off the absence of key midfielders Declan Rice and Martin Odegaard to remain undefeated this season and close within two points of leaders Manchester City.
Brentford had the perfect start when Yoane Wissa opened the scoring 22 seconds after kickoff to stun the Etihad Stadium but Haaland restored parity in the 19th minute when he scored from a tight angle with just his second touch of the game.
The home side dominated the opening half and Luis Diaz hit a post in the 17th minute, but too often the Liverpool attackers found themselves on different wavelengths, and much of their play lacked their usual fluidity as chances went begging.
Alejandro Garnacho added a late goal for Erik ten Hag's side who started the day 14th in the standings after back-to-back losses. They now have six points from four matches while newly promoted Southampton remain without a point.
The Egyptian, who is the highest scoring visiting player to Old Trafford in Premier League history with seven goals, netted and provided two assists for Luis Diaz as Liverpool continued life under new boss Arne Slot in perfect fashion this season.
Enzo Maresca's Chelsea have won only once in the first three league games of the Italian's reign after a chaotic close-season.
The 24-year-old Norwegian scored his 11th hattrick for City to extend the champions' perfect start to their title defence, notching up his seventh goal in three league games this season.
Zirkzee came off the bench in the second half at Old Trafford on Friday and delivered a memorable first impression as his 87th-minute strike gave United the perfect start to the new season.