Liverpool made it five wins from five in the Premier League after coming from behind to beat Newcastle United 3-1 at Anfield, while Manchester United earned a first victory since the opening weekend of the season by beating Leicester City.
Chelsea and Tottenham Hotspur were much more emphatic, however, with a hat-trick from Tammy Abraham firing Frank Lampard's side to a 5-2 win at Wolverhampton Wanderers, while first-half goals gave Spurs a 4-0 win over Crystal Palace.
With champions Manchester City at Norwich City later on Saturday, Liverpool looked to extend their lead at the top to five points, but Anfield was stunned into silence early on as Jetro Willems thundered Newcastle into a shock lead.
Going behind does not faze a relentless Liverpool side that had won each of the last four league games in which they had conceded first, and soon enough Sadio Mane had brilliantly restored parity in the Merseyside sunshine.
Roberto Firmino came off the bench to replace the injured Divock Origi to set up Mane for the second goal, before the Brazilian delightfully flicked the ball through for Mo Salah to seal a 14th consecutive league win for the hosts.
Manchester United have suffered plenty of woes from the penalty spot this season, having missed two spot kicks already this campaign.
Marcus Rashford was the last of those to miss against Southampton, but the young striker stepped up from 12 yards against Leicester after he was felled in the penalty area in the eighth minute at Old Trafford to put United in front.
Chelsea had endured a difficult start to the season ahead of a tough trip to Wolves, but three goals in 10 first-half minutes put them in command at Molineux.
Abraham completed his first Premier League hat-trick in the second half to take his goal tally to seven atop the Premier League scoring charts, but his eventful afternoon was not over there as he then put through his own net.
Spurs were another side without a win since the opening weekend ahead of the visit of a Palace team who had won their last two league games, but a Son Heung-min double helped the hosts race into a 3-0 lead inside 24 minutes.
Argentine forward Erik Lamela added a fourth before the interval as Tottenham strolled to victory.
Moussa Djenepo'a strike gave Southampton a 1-0 win at promoted Sheffield United, while a last-gasp equaliser from Jeff Hendrick earned Burnley a 1-1 draw at Brighton & Hove Albion.
Scoreboard
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Afghanistan innings
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R. Gurbaz lbw b Williams 43
H. Zazai c Williams b Chatara 13
N. Tarakai c Ndlovu b Williams 14
A. Afghan c Burl b Ndlovu 14
N. Zadran not out 69
M. Nabi c Burl b Chatara 38
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Extras (b2, w3, nb1) 6
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Total: (5 wkts, 20 overs) 197
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Did not Bat: Gulbadin Naib, Rashid Khan, Mujeeb Ur Rahman, Karim Janat, Fareed Malik
Fall of wickets: 1-57 (Zazai), 2-60 (Gurbaz), 3-80 (Tarakai), 4-90 (Afghan), 5-197 (Nabi)
Bowling: Ndlovu 4-0-35-1, Jarvis 4-0-53-0, Chatara 4-0-53-2, Williams 4-0-16-2 (w2), Burl 1-0-4-0, Madziva 3-0-34-0 (w1, nb1)
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Zimbabwe innings
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B. Taylor c Zazai b Fareed 27
H. Masakadza run out 3
C. Ervine lbw b Karim 10
S. Williams c Gurbaz b Fareed 0
T. M. Tarakai b Rashid 20
R. Burl b Rashid 25
R. Chakabva not out 42
N. Madziva c Nabi b Naib 15
K. Jarvis not out 15
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Extras: (b1, lb 5, nb2, w4) 12
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Total: (7 wkts; 20 overs) 169
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