Bruno Fernandes starred with a hat-trick in Manchester United's 5-2 rout of Ipswich, while Chelsea extended Xabi Alonso's perfect start with a thrilling 4-3 win against Brighton on Sunday.
Fernandes shone as he ensured United bounced back from their humiliating 2-0 defeat at Hull on the opening weekend of the Premier League season.
Boss Michael Carrick was in danger of another embarrassing loss to a promoted club when Leif Davis put Ipswich ahead at Old Trafford with a 29th-minute strike that cannoned in off the crossbar.
But the Fernandes show started in the 40th minute after Marcelino Nunez's slip allowed Matheus Cunha to pick out the United captain for a sumptuous finish.
United went in front in the 56th minute when Jacob Greaves was pressured into an own goal.
Greaves deflected Harry Maguire's shot into his own net, with Ipswich's appeals for handball against the United defender snubbed by VAR.
Completing a miserable five minutes for Greaves, the Ipswich defender conceded a penalty with his foul on Cunha and United captain Fernandes stepped up to slot home from the spot.
Fernandes sealed his treble in the 68th minute, sweeping in from close-range after Kobbie Mainoo and Bryan Mbeumo had shots blocked.
It was Fernandes's second league hat-trick for United following his treble against Leeds five years ago.
Fernandes was not finished, and Bryan Mbeumo scored from his pass with a lob that clipped the bar and dropped over the line in the 82nd minute.
Chuba Akpom's stoppage-time tap-in was little consolation for outclassed Ipswich, who were beaten for the first time since returning to the top flight.
"It was a massive result for us. We lost three points last week. First game at home, the fans have been waiting for this," Fernandes said.
"Scoring goals is the best feeling in football. Doing a hat-trick at home with our fans is something I'm proud of. I hope I can do much more and help my teammates score too."
PALMER GENIUS
Joao Pedro, Morgan Rogers and Cole Palmer all scored when Alonso's reign as Chelsea boss kicked off with a 3-2 win at Fulham on Monday.
And Pedro and Palmer were back on target, while Rogers teed up Chelsea's second goal, scored by Pedro Neto, as the Blues held off a rally from Brighton at Stamford Bridge.
Emiliano Martinez made his Chelsea debut in goal just hours after sealing his move from Aston Villa.
But there was no place for his Argentina teammate Enzo Fernandez, who could still leave Chelsea for Manchester City before Tuesday's transfer deadline.
"We have to be aware until Tuesday evening what is going to develop. We're not sure. We are preparing for all scenarios," Alonso said of Fernandez.
"I'm sure that, whatever happens, from Wednesday we will have a good enough squad to compete in the Premier League."
Romeo Lavia profited from a mix-up between Bart Verbruggen and Mats Wieffer to prod in Chelsea's opening goal from a corner.
Neto then turned in Rogers's cross before Pedro rounded off a brilliant Chelsea counter-attack that began inside their own box.
Martinez was beaten moments later by a blistering volley from Malick Yalcouye.
Pedro turned Pascal Gross's cross into his own net just after the hour mark.
A moment of genius from Palmer eased Chelsea's nerves as he curled into the bottom corner from outside the area after a fine solo run.
Gross headed in a stoppage-time consolation for Brighton, but Chelsea join Manchester City and Hull as the only sides to take six points from their opening two games.
Brentford were on course to also maintain their perfect start when Kevin Schade's audacious flick opened the scoring away to Leeds.
But Dominic Calvert-Lewin turned in Lukas Nmecha's driven cross to salvage a point and Leeds's unbeaten start to the campaign.
Sunderland got off the mark with a 1-0 victory over Fulham thanks to Wilson Isidor's winner 15 minutes from time.