Bayern's only representative in the player poll was Thiago Alcantara, in fourth, after he scored an acrobatic scissor kick in injury time for a 2-1 win against Stuttgart on Wednesday.
Costa, the players' poll leader for the second time this season, scored in Atletico's 4-0 rout of Real Sociedad, sending the side three points clear atop of the Spanish league.
The victory came after Atletico fans paid tribute to former player and coach Luis Aragones, whose death was announced on Saturday.
"Remarkably, this is the first time that Atletico Madrid have led Spain's La Liga outright since winning the title eighteen years ago," Chris Tait of The Herald in Scotland said. "It would seem a fitting tribute to Luis Aragones."
Atletico polled second among the clubs, six points behind Bayern. Its emphatic win over Frankfurt meant it was 13 points ahead of second-place Bayer Leverkusen, a winner of 17 out of 19 league games and unbeaten in 44 games overall.
Valencia was third for beating Barcelona, Juventus fourth after beating Inter Milan 3-1, and Chelsea fifth, for inflicting a first home defeat on Manchester City in a tactical masterclass from coach Jose Mourinho.
"Chelsea were magnificent ... thanks to a brilliant performance, a great team spirit and an intelligent tactical plan," Aurelio Capaldi of RAI Sports in Italy said. "Eden Hazard (third in the player vote) was superb and Nemanja Matic made things heated for Yaya Toure, but this is Jose Mourinho's triumph as he made the right choices, prepared the game perfectly, and showed yet again an amazing talent for exploiting the rivals' weaknesses."
James Porteous of The South China Morning Post believes Chelsea can challenge for the Premier League title, despite Mourinho suggesting after the win that his side will not be ready to do so until next season.
"For all Jose Mourinho's insistence that his team aren't title contenders, he will be telling them something very different in the privacy of the dressing room," Porteous said.
Alex Oxlade-Chamberlain was second in the player vote after scoring both goals in Arsenal's 2-0 win over Crystal Palace and leading the Gunners back to the top of the English Premier League.
Rounding out the top five were Chelsea's Eden Hazard, Alcantara, and Atalanta's German Denis.
Denis scored twice in the 3-0 win over his former club Napoli.
AP Global Soccer 10 rankings, week ending Feb. 4
1. Diego Costa, 99 points.
2. Alex Oxlade-Chamberlain, 80.
3. Eden Hazard, 79.
4. Thiago Alcantara, 62.
5. German Denis, 61.
6. Charlie Adam, 58.
7. Andrea Pirlo, 50.
8. Wesley Sneijder, 43.
9. Daniel Parejo, 38.
10. Pierre-Emerick Aubameyang, 34.
1. Bayern Munich, 143.
2. Atletico Madrid, 137.
3. Valencia, 130.
4. Juventus, 115.
5. Chelsea, 107.
6. Arsenal, 56.
7. Stoke, 47.
8. Atalanta, 42.
9. Paris Saint-Germain, 41.
10. Sunderland, 34.