There were big wins for Manchester City and Arsenal, while the likes of Manchester United, Liverpool and Newcastle also started their respective campaigns with important victories.
As always, Flashscore will be selecting a Team of the Week based on our player ratings system - picking out the 11 best performers from the weekend's action.
GK: Neto, 7.8 (Bournemouth)
Neto excelled between the sticks during Bournemouth's 1-1 draw against Nottingham Forest, making seven saves to ensure his side came away with a point in a tough opening fixture.
The Brazilian helped to keep Forest at bay as the Cherries searched for an equaliser throughout most of the match before eventually being rewarded for his mammoth efforts as Antoine Semenyo netted a late leveller.
DEF: Pedro Porro, 7.9 (Tottenham Hotspur)
Spurs opened their campaign with a 1-1 draw against newly promoted Leicester on Monday evening - a disappointing result after dominating the majority of the first half.
Pedro Porro opened the scoring at the King Power Stadium, ghosting into the area to head home and give his side a deserved lead.
The Spaniard was a threat throughout, making four key passes as the London club created several chances against the Foxes, just not enough for a second goal.
DEF: Nathan Collins, 7.9 (Brentford)
Irishman Nathan Collins put in a superb defensive performance for Brentford in their 2-1 opening-day win against the much-fancied Crystal Palace.
The defender made six clearances, five tackles, two blocks and won eight duels against a very tricky Palace attack, keeping the likes of Jean-Philippe Mateta, Daichi Kamada and Eberechi Eze at bay.
DEF: Noussair Mazraoui, 7.6 (Manchester United)
Debutant Noussair Mazraoui was thrust into Manchester United's defence just days after signing from Bayern Munich and put in a top performance during their 1-0 win against Fulham.
Mazraoui was a constant threat along the right-hand side and linked up well with Amad Diallo, causing plenty of issues for the Fulham defence.
He also fulfilled his defensive duties, making three interceptions, two clearances and two tackles.
MID: Savinho, 8.0 (Manchester City)
Savinho only played the first 45 minutes of Manchester City's 2-0 win away at Chelsea but proved he will have a big role in the coming season after an excellent showing.
The Brazilian completed all three of his attempted dribbles, made three key passes and won five ground duels in an impressive performance - proving he is already capable of mixing it with the rest of City's star attackers.
MID: Mateo Kovacic, 8.1 (Manchester City)
Another top performer in City's win at Stamford Bridge, Mateo Kovacic returned to haunt his former club with a late goal to seal three points for his side.
Despite missing stalwart Rodri as his midfield partner, Kovacic put in a typically solid showing as City laid out a marker for the rest of the campaign with a deserved victory.
MID: Alex Scott, 8.3 (Bournemouth)
Alex Scott put in a brilliant all-round display during Bournemouth's draw against Forest, having an impact at both ends of the pitch.
The youngster completed 90% of his passes and played one key ball while also winning 13 duels as well as making eight tackles, three interceptions and two clearances.
MID: Amadou Onana, 8.2 (Aston Villa)
Aston Villa's Amadou Onana had a debut to remember against West Ham, scoring just minutes into the game with a towering header from a corner.
The Belgian went on to dominate the midfield with a superb performance, providing a good shield for the Villa defence while also helping his team get up the pitch when the opportunity arose.
Onana was typically strong in the tackle while also very tidy on the ball, completing 30 of his 31 attempted passes as Villa came out 2-1 victors.
MID: Joelinton, 8.0 (Newcastle)
An opening day home clash against relegation favourites Southampton could have quickly turned sour for Newcastle after Fabian Schar was sent off midway through the first half, but Joelinton was on hand to ensure the Magpies still came away with three points.
Eddie Howe's side won 1-0 after an excellent finish from the Brazilian, who helped to capitalise on a poor mistake by Saints goalkeeper Alex McCarthy.
Joelinton was equally effective at the other end of the pitch, helping Newcastle to see out their win despite being a man down for over an hour.
FWD: Bukayo Saka, 8.5 (Arsenal)
Bukayo Saka bagged a goal and an assist in Arsenal's 2-0 win against Wolves, first setting up Kai Havertz's opener before cutting inside and firing in himself for the Gunners' second.
He also created plenty of other chances, making five key passes before being substituted after 80 minutes.
The young winger set his stall out for the season early on with a fantastic display, earning him an 8.5 player rating - the highest of any Premier League player on the opening weekend.
FWD: Kai Havertz, 8.2 (Arsenal)
Rounding off our side this week is Kai Havertz, who also got a goal and assist in Arsneal's win against Wolves.
The German opened his account for the season with a powerful header from Saka's cross before going on to set up his partner midway through the second half - helping to ensure the Gunners started their campaign with a solid win.