Rickie Lambert's dream week continued as he helped Southampton to win at West Bromwich Albion and Liverpool started the new campaign with three points.
Roberto Martinez picked up a point in his first match as Everton manager, while the summer revolution at Sunderland got off to a rocky start following defeat by Fulham.
Manchester United kicked off the defence of their title, and a new era, with an eye-catching 4-1 win at Swansea thanks to braces from Robin van Persie and Danny Welbeck.
In an open game, United took the lead on 34 minutes when Van Persie was played onside and he controlled Ryan Giggs' lofted pass before acrobatically volleying past Michel Vorm.
Just two minutes later, the lead was doubled as Patrice Evra's cross was helped back by Antonio Valencia and Welbeck had the simple task of scoring from a couple of yards.
Wayne Rooney was introduced as a second-half substitute and he was involved in the third goal on 71 minutes as he passed to Van Persie, who ran to the edge of the penalty area and used the dummy runners before firing an unstoppable shot past Vorm.
Swansea pulled a goal back that their performance deserved on 82 minutes when half-time substitutes Pablo Hernandez and Wilfried Bony combined for the latter to steer his shot beyond David de Gea.
But United had the final word two minutes into stoppage time when Welbeck impudently chipped Vorm from Rooney's pass to double his Premier League tally from last season.
Cardiff were given an early warning of how tough life in the top flight will be after going down 2-0 to West Ham at Upton Park.
West Ham were much the better team in the first half and were rewarded on 13 minutes when Matt Jarvis pulled the ball back to Joe Cole, who turned and fired a low shot into the corner.
A second goal finally arrived 16 minutes from time when Mark Noble drove towards the penalty area before teeing up Kevin Nolan to sweep home beyond David Marshall.
Christian Benteke scored a goal in each half as Arsenal had Laurent Koscielny sent off in Aston Villa's impressive 3-1 win at Emirates Stadium.
Slack defending contributed to Arsenal's opener on six minutes when Alex Oxlade-Chamberlain got down the left wing and his low cross was converted by the unmarked Olivier Giroud at the near post.
Villa were level midway through the first half when Gabriel Agbonlahor was brought down in the penalty area by Wojciech Szczesny. The Arsenal keeper briefly redeemed himself by saving Christian Benteke's spot-kick, but the Belgium international reacted the quickest to head home the rebound.
Fabian Delph struck the post for Villa early in the second half before the visitors took the lead on 61 minutes after Arsenal conceded another penalty.
Koscielny was booked for bringing down Agbonlahor and this time Benteke made no mistake as he sent Szczesny the wrong way.
Just six minutes later, Koscielny was sent off after picking up a second yellow card and Villa took advantage five minutes from time to score a third when Antonio Luna broke clear to finish clinically past Szczesny.
Simon Mignolet saved a late penalty as Liverpool beat Stoke City 1-0 in the opening game of the Premier League season thanks to Daniel Sturridge's goal.
Robert Huth volleyed against the crossbar for Stoke, and summer signing Kolo Toure was then denied by the woodwork for Liverpool.
The breakthrough came on 37 minutes when Sturridge cushioned an Iago Aspas pass before drilling a low shot through the legs of Huth to beat Asmir Begovic.
With minutes to go, Daniel Agger handled former Reds midfielder Charlie Adam's free-kick, but Mignolet dived low to his right to push away Jon Walters' penalty and he then denied Kenwyne Jones from the follow-up.
Everton's new era under Martinez started with a 2-2 draw at Carrow Road as Ricky van Wolfswinkel marked his Norwich debut with a fine equaliser.
Norwich took the lead on 51 minutes when Steven Whittaker enjoyed the bounce of the ball and, after his excellent curler came back off the post, he tucked away the loose ball.
But Everton were level 10 minutes later when Seamus Coleman's industry teed up Ross Barkley to take a touch and hammer home from 25 yards.
And four minutes later Everton were in front when Nikica Jelavic's shot was parried out by John Ruddy to Coleman, who finished confidently.
Norwich hit back on 71 minutes, though, when Whittaker's wild volley turned into the perfect cross for record signing Van Wolfswinkel to head into the corner.
Fresh from scoring on his England debut, Lambert made it a week to remember as his late penalty earned Southampton a 1-0 success at West Brom.
Southampton thought they had taken the lead on the half-hour mark when Lambert's header across goal was cushioned home by Adam Lallana, but the midfielder was adjudged, perhaps harshly, to be offside.
In the final minute, Southampton were gifted the winner when Luke Shaw was brought down by Youssouf Mulumbu and Lambert stepped up to convert the penalty.
Paolo Di Canio has overhauled the Sunderland squad over the summer, but he could only watch on as Fulham pinched a 1-0 win at the Stadium of Light.
Sunderland had come closest to scoring in the first half, but conceded decisively on 52 minutes when Damien Duff's corner was headed home at the far post by Pajtim Kasami.