Robert Lewandowski gave 10-man Bayern Munich a last-minute victory in the Bundesliga, while Wayne Rooney recorded his 10th straight game without a goal for Manchester United in the Premier League on Saturday.
With the Spanish league and Italy's Serie A also under way, here is a look at Europe's major leagues on Saturday:
As Rooney continues to struggle, an English striker did manage to score a hat trick: Callum Wilson of promoted Bournemouth.
Wilson helped Bournemouth beat West Ham 4-3 for its first ever win in the top flight of English football.
Rooney, meanwhile, has now gone 10 games without a goal for United, which was held to a 0-0 draw with Newcastle.
Also, Tottenham drew 1-1 at Leicester, while Jermain Defoe secured Sunderland's first point of the season by equalizing in a 1-1 draw with Swansea.
Crystal Palace also beat Aston Villa 2-1, and Stoke drew 1-1 at Norwich.
Bayern Munich conceded a goal after just nine seconds but Lewandowski's late goal secured a 2-1 win over Hoffenheim. Forward Kevin Volland capitalized on a poor back pass from Bayern's David Alaba to match the fastest German league goal ever scored.
Thomas Mueller equalized by pushing in a rebound with his right thigh in the 41st minute, and Bayern overcame Jerome Boateng's sending off in the 73rd for a handball in the area as Eugen Polanski struck the resulting penalty against the post. That led to a final push from Bayern and Lewandowski netted the winner after a pass from Douglas Costa.
Elsewhere, Hamburger SV twice came from behind to beat Stuttgart 3-2. Bayer Leverkusen won 1-0 at Hannover, promoted Darmstadt held Schalke to a 1-1 draw, and Eintracht Frankfurt drew 1-1 with Augsburg.
On the opening day in Serie A, Roma was held 1-1 at Hellas Verona while Lazio beat newly-promoted Bologna 2-1.
Bosko Jankovic volleyed Verona into the lead on the hour but its advantage lasted barely five minutes before Alessandro Florenzi leveled for Roma with a long-range strike.
Lazio took the lead in the 18th when Bologna's defense failed to deal with Dusan Basta's cross and the onrushing Lucas Biglia smashed it home.
Bologna gifted Lazio the second, too, as it allowed Antonio Candreva's cross to go through to Ricardo Kishna, who had plenty of time and space to control and shoot.
Matteo Mancosu reduced the deficit on the stroke of halftime.
Goals from free kicks gave Atletico Madrid a slim win over promoted Las Palmas and helped Espanyol beat 10-man Getafe as the Spanish league struggled to produce scoring on its opening weekend.
Atletico settled for a 1-0 victory thanks to Antoine Griezmann's free kick in the 16th minute at its Vicente Calderon Stadium.
In Barcelona, Espanyol midfielder Salva Sevilla secured a 1-0 win with a dipping free kick that went in off the upright in the third minute.
Elsewhere, the Spanish league saw two more 0-0 draws after Valencia stalled at Rayo Vallecano and Real Sociedad split the points at Deportivo La Coruna.
Both matches were similar to Friday's league opener when Sevilla and Malaga looked rusty after the summer in their 0-0 draw.
Lyon fell to its first defeat of the season, losing 2-1 at home to Rennes as Mehdi Zeffane set up the opener before scoring the winner against his former club.
Reims and Caen failed to maintain their perfect start to the season as they lost 1-0 at Nantes and 2-1 at Nice, respectively.
Julian Palmieri struck twice in the first half to send Bastia on its way to a 3-0 win at Guignamp.
Angers maintained its third clean sheet in as many games as Cheikh N'Doye scored two first-half goals for a 2-0 victory at Ajaccio.
Monaco failed to boost its confidence ahead of the second leg of its Champions League playoff against Valencia - where it trails 3-1 - as it drew 1-1 at Toulouse.