Messi opened the scoring with a solo effort as Barcelona won 2-0 at promoted Almeria to make it seven wins out of seven in La Liga and set a club record start to a campaign but the Argentine went off with a hamstring injury that will keep him out for up to three weeks.
Atletico, who also have a perfect record, are in second place on goal difference after an impressive 1-0 derby win at Real thanks to an 11th-minute strike from Diego Costa which took his league tally to eight, the same as Messi.
Real were left five points off the pace back in third on 16 points, two ahead of fourth-placed Villarreal who lost 1-0 at Real Betis on Sunday.
Leaders AS Roma kept up their 100 percent record in style, thrashing Bologna 5-0 on a stormy night at the Stadio Olimpico for their sixth successive win of the season.
Champions Bayern Munich and Borussia Dortmund, both unbeaten, stayed neck and neck at the top of the Bundesliga with 19 points from a possible 21 after contrasting home wins.
Dortmund thrashed 10-man Freiburg 5-0 with two goals each from Marco Reus and Robert Lewandowski and one from Jakub Blaszczykowski. The winless visitors had Fallou Diagne sent off just before half-time.
Last season's treble winners Bayern needed a second-half goal from Thomas Mueller to scrape past VfL Wolfsberg.
A clever Joao Moutinho free kick kept Monaco top of Ligue 1 despite a 1-1 draw at Stade Reims.
The principality club are ahead on goal difference from champions Paris St Germain, who beat Toulouse 2-0 at home with goals from Marquinhos and Edinson Cavani, his fourth of season.
PSG played with a revamped squad ahead of Wednesday's Champions League home clash against Benfica but produced a mediocre performance.
Olympique Marseille, who visit Borussia Dortmund on Tuesday, were not at their best either but last year's runner-ups did enough to win 2-0 at Lorient and stay third, one point adrift.
Substitute Luciano Figueroa hit the winner as stuttering Panathinaikos claimed a 2-1 home win against Asteras Tripolis to go third in the table on Sunday.
Swedish forward Marcus Berg's third goal of the season was levelled by a long-range drive from Tripolis's Argentine midfielder Pablo De Blasis before Figueroa struck after 74 minutes.
Panathinaikos have 11 points from six matches, two points behind second-placed PAOK Salonika, who drew 1-1 with OFI Crete, and five adrift of leaders Olympiakos Piraeus who meet Anderlecht in Belgium on Wednesday in the Champions League.
In Crete, PAOK went behind after 15 minutes when Alexandros Perogamvrakis scored but Tomas Necid levelled with 16 minutes to go.
AZ Alkmaar beat league leaders PSV Eindhoven 2-1 and then sacked coach Gertjan Verbeek, citing "a lack of chemistry" between him and the squad.
Twente Enschede took over at the top on Sunday on goal difference after dismantling FC Groningen 5-0 thanks to two goals from Ghana teenager Shadrach Eghan,
Enschede have 15 points alongside PSV and Heerenveen.
Alfred Finnbogason scored his 10th goal of the season for Heerenveen, netting the winner in their 2-1 derby win over Cambuur Leeuwarden.