Robin van Persie and Danny Welbeck scored twice each as champions United eased to a 4-1 win at Swansea City while Oscar and Frank Lampard grabbed the goals to lift Chelsea to a 2-0 victory over promoted Hull City.
Last season's runners-up Manchester City host Newcastle United on Monday.
Treble winners Bayern Munich beat Eintracht Frankfurt 1-0 courtesy of a Mario Mandzukic volley on Saturday to equal their club record of 27 straight league games without defeat.
They are one of five teams who have won their opening two Bundesliga matches alongside Borussia Dortmund, Bayer Leverkusen, Mainz 05 and Werder Bremen.
Borussia Dortmund, runners-up to Bayern in both the Champions League and Bundesliga last season, beat promoted Eintracht Braunschweig 2-1.
Schalke 04 crashed to a 4-0 defeat at VfL Wolfsburg and Hamburg SV fared even worse as they were mauled 5-1 at home by Hoffenheim.
Carlos Tevez scored on his Juventus debut as the Serie A champions crushed last season's Coppa Italia winners Lazio 4-0 to win the Supercup.
Striker Kolbeinn Sigthorsson scored both goals as champions Ajax Amsterdam won an early season meeting with arch rivals Feyenoord 2-1.
Ajax recovered from a goal behind to win the match regarded as the Dutch league season's 'classic' to claim a second win in three matches this season while Feyenoord suffered third successive loss - their worst ever start to a season.
PEC Zwolle, who won 5-1 at NEC Nijmegen, and PSV Eindhoven, who beat Go Ahead Eagles 3-0, are the only teams to have won all three games so far.
A late goal by Edinson Cavani, his first in Ligue 1, salvaged a point for Paris St Germain in 1-1 with Ajaccio.
The defending champions have two points from two games, already trailing rivals Monaco by four after the big-spending club crushed Montpellier 4-1 thanks to a Radamel Falcao goal and Emmanuel Riviere's first hat-trick of his career.
Last year's runners-up Olympique Marseille beat Evian Thonon Gaillard 2-0 at home and are one of the four teams to maintain a perfect start along with Monaco, Olympique Lyon and St Etienne.
Panathinaikos opened the season with a 2-0 win over Panaitolikos on their return to the Apostolos Nikolaidis stadium.
The Greens, under new coach Giannis Anastasiou, were playing their first game at the renovated ground since 2008 after switching back from the Olympic Stadium.
PAOK Salonica, last season's runners-up, beat Skoda Xanthi 3-0. Reigning champions Olympiakos visit promoted AEL Kallonis on Monday
Titleholders Austria Vienna produced their best performance of the season so far as they demolished Wiener Neustadt 5-0 with Philipp Hosiner scoring twice.
Leaders Salzburg drew 1-1 at Sturm Graz to remain unbeaten after five games. Spaniard Jonatan Soriano scored Salzburg's goal to take his season tally to seven goals. Rapid Vienna lost their first game of the season, going down 2-0 at Admira Modling.
Leaders Standard Liege maintained their 100 percent record after four games when an own goal by Ludovic Buysens gave them a 1-0 win over OH Leuven.
Fram Reykjavik won the Icelandic Cup for the eighth time, and the first in 24 years, after beating Stjarnan 3-2 on penalties following a 3-3 draw in the final.
Stjarnan, also beaten in last year's final, led 2-0 at halftime and 3-2 with only four minutes to go before Almarr Ormarsson's second goal of the game made it 3-3 and took the match to extra-time. ($1 = 0.7500 euros)